Multiplicity results for elliptic problems with variable exponent and nonhomogeneous Neumann conditions
Applying three critical point theorems, we prove the existence of at least three weak solutions for a class of differential equations with p(x)‐Laplacian and subject to small perturbations of nonhomogeneous Neumann conditions. Copyright © 2014 John Wiley & Sons, Ltd.
Saved in:
| Published in | Mathematical methods in the applied sciences Vol. 38; no. 12; pp. 2589 - 2599 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Freiburg
Blackwell Publishing Ltd
01.08.2015
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0170-4214 1099-1476 |
| DOI | 10.1002/mma.3244 |
Cover
| Abstract | Applying three critical point theorems, we prove the existence of at least three weak solutions for a class of differential equations with p(x)‐Laplacian and subject to small perturbations of nonhomogeneous Neumann conditions. Copyright © 2014 John Wiley & Sons, Ltd. |
|---|---|
| AbstractList | Applying three critical point theorems, we prove the existence of at least three weak solutions for a class of differential equations with p(x)‐Laplacian and subject to small perturbations of nonhomogeneous Neumann conditions. Copyright © 2014 John Wiley & Sons, Ltd. Applying three critical point theorems, we prove the existence of at least three weak solutions for a class of differential equations with p ( x )‐Laplacian and subject to small perturbations of nonhomogeneous Neumann conditions. Copyright © 2014 John Wiley & Sons, Ltd. Applying three critical point theorems, we prove the existence of at least three weak solutions for a class of differential equations with p(x)-Laplacian and subject to small perturbations of nonhomogeneous Neumann conditions. |
| Author | Heidarkhani, Shapour Afrouzi, Ghasem A. Hadjian, Armin |
| Author_xml | – sequence: 1 givenname: Shapour surname: Heidarkhani fullname: Heidarkhani, Shapour email: Correspondence to: Shapour Heidarkhani, Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran., s.heidarkhani@razi.ac.ir organization: Department of Mathematics, Faculty of Sciences, Razi University, 67149, Kermanshah, Iran – sequence: 2 givenname: Ghasem A. surname: Afrouzi fullname: Afrouzi, Ghasem A. organization: Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran – sequence: 3 givenname: Armin surname: Hadjian fullname: Hadjian, Armin organization: Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, Iran |
| BookMark | eNp1kE1v1DAQhi1UJLYFiZ9giQuXLHbsfPhYFiiVdrcCgThak2TSuiR2sB3a_fd4u1UrED2NRnpm5pn3mBxZZ5GQ15wtOWP5u3GEpcilfEYWnCmVcVmVR2TBeMUymXP5ghyHcM0YqznPF-RyMw_RTINpTdxRjyG1gfbOUxwGM0XT0sm7ZsAx0BsTr-hv8AZST_F2SpdtpGA7miSu3Ogu0aKbA93iPIK1tHW2M9E4G16S5z0MAV_d1xPy_dPHb6vP2fri7Hx1us5aKaTMJDJouBBFzztAWaqWFY0qOlQ99n1d9QBt1yhZK5RQQdvkSuZF3THFpICyECfk7WFvsv41Y4h6NKFNv8CdmeYVr1UhBK8S-uYf9NrN3iY7zUtVskLW5Z5aHqjWuxA89jolBfufogczaM70Pnedctf73B8NHgYmb0bwu_-h2QG9MQPunuT0ZnP6N29CxNsHHvxPnUyrQv_Ynulcfv2w-rJd6_fiD1y7pNg |
| CODEN | MMSCDB |
| CitedBy_id | crossref_primary_10_1007_s12591_017_0345_y crossref_primary_10_1515_msds_2020_0108 crossref_primary_10_3103_S106836232201006X crossref_primary_10_1002_mana_201900123 crossref_primary_10_54503_0002_3043_2022_57_1_64_76 crossref_primary_10_52846_ami_v48i1_1365 |
| Cites_doi | 10.21136/CMJ.1991.102493 10.1016/j.na.2010.12.013 10.1016/j.matpur.2007.10.006 10.1016/j.na.2009.03.009 10.3934/dcdss.2012.5.753 10.1007/s11565-006-0002-9 10.1016/j.na.2012.05.009 10.1016/j.na.2004.09.026 10.1006/jmaa.2000.7617 10.1016/S0377-0427(99)00269-1 10.1016/j.na.2009.05.007 10.1007/BFb0104029 10.1006/jmaa.2001.7618 10.1155/2009/670675 10.1016/j.jde.2008.02.025 10.1016/j.na.2006.09.060 10.1070/IM1987v029n01ABEH000958 10.1016/j.jmaa.2010.09.050 10.1017/CBO9780511760631 10.14232/ejqtde.2013.1.24 10.1080/17476933.2012.662225 10.1080/00036810903397438 10.1016/j.aml.2010.03.015 10.1155/2010/564363 10.1137/050624522 10.1002/mana.200810232 10.1002/mma.1568 |
| ContentType | Journal Article |
| Copyright | Copyright © 2014 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd. |
| Copyright_xml | – notice: Copyright © 2014 John Wiley & Sons, Ltd. – notice: Copyright © 2015 John Wiley & Sons, Ltd. |
| DBID | BSCLL AAYXX CITATION 7TB 8FD FR3 JQ2 KR7 |
| DOI | 10.1002/mma.3244 |
| DatabaseName | Istex CrossRef Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts |
| DatabaseTitle | CrossRef Civil Engineering Abstracts Engineering Research Database Technology Research Database Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection |
| DatabaseTitleList | CrossRef Civil Engineering Abstracts Civil Engineering Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Sciences (General) Mathematics |
| EISSN | 1099-1476 |
| EndPage | 2599 |
| ExternalDocumentID | 3742643641 10_1002_mma_3244 MMA3244 ark_67375_WNG_24RDCQNL_B |
| Genre | article |
| GroupedDBID | -~X .3N .GA .Y3 05W 0R~ 10A 1L6 1OB 1OC 1ZS 31~ 33P 3SF 3WU 4.4 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5GY 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHQN AAMMB AAMNL AANHP AANLZ AAONW AASGY AAXRX AAYCA AAZKR ABCQN ABCUV ABIJN ABJNI ABPVW ACAHQ ACBWZ ACCZN ACGFS ACIWK ACPOU ACRPL ACSCC ACXBN ACXQS ACYXJ ADBBV ADEOM ADIZJ ADKYN ADMGS ADNMO ADOZA ADXAS ADZMN AEFGJ AEIGN AEIMD AENEX AEUYR AEYWJ AFBPY AFFPM AFGKR AFWVQ AFZJQ AGHNM AGQPQ AGXDD AGYGG AHBTC AIDQK AIDYY AIQQE AITYG AIURR AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN ALVPJ AMBMR AMVHM AMYDB ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BSCLL BY8 CO8 CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS EJD F00 F01 F04 F5P FEDTE G-S G.N GBZZK GNP GODZA H.T H.X HBH HF~ HGLYW HHY HVGLF HZ~ IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES M6O MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 NF~ O66 O9- OIG P2P P2W P2X P4D PALCI Q.N Q11 QB0 QRW R.K RIWAO RJQFR ROL RX1 RYL SAMSI SUPJJ UB1 V2E W8V W99 WBKPD WH7 WIB WIH WIK WOHZO WQJ WXSBR WYISQ XBAML XG1 XPP XV2 ZZTAW ~02 ~IA ~WT AAHHS ACCFJ AEEZP AEQDE AEUQT AFPWT AIWBW AJBDE RWI RWS WRC AAYXX CITATION 7TB 8FD FR3 JQ2 KR7 |
| ID | FETCH-LOGICAL-c4344-4e0ab1335f1dae469c05b95de9feff87faacdb9489e4a7acb294258d09043a653 |
| IEDL.DBID | DR2 |
| ISSN | 0170-4214 |
| IngestDate | Fri Jul 11 06:37:19 EDT 2025 Fri Jul 25 12:16:19 EDT 2025 Tue Jul 01 00:19:00 EDT 2025 Thu Apr 24 23:03:24 EDT 2025 Wed Jan 22 16:41:58 EST 2025 Sun Sep 21 06:18:38 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 12 |
| Language | English |
| License | http://onlinelibrary.wiley.com/termsAndConditions#vor |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c4344-4e0ab1335f1dae469c05b95de9feff87faacdb9489e4a7acb294258d09043a653 |
| Notes | ark:/67375/WNG-24RDCQNL-B ArticleID:MMA3244 istex:2921B2E95EF4892235179CD6D37C8645FC28A4DC ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 |
| ORCID | 0000-0002-6327-918X |
| PQID | 1696054867 |
| PQPubID | 1016386 |
| PageCount | 11 |
| ParticipantIDs | proquest_miscellaneous_1718953317 proquest_journals_1696054867 crossref_citationtrail_10_1002_mma_3244 crossref_primary_10_1002_mma_3244 wiley_primary_10_1002_mma_3244_MMA3244 istex_primary_ark_67375_WNG_24RDCQNL_B |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | August 2015 |
| PublicationDateYYYYMMDD | 2015-08-01 |
| PublicationDate_xml | – month: 08 year: 2015 text: August 2015 |
| PublicationDecade | 2010 |
| PublicationPlace | Freiburg |
| PublicationPlace_xml | – name: Freiburg |
| PublicationTitle | Mathematical methods in the applied sciences |
| PublicationTitleAlternate | Math. Meth. Appl. Sci |
| PublicationYear | 2015 |
| Publisher | Blackwell Publishing Ltd Wiley Subscription Services, Inc |
| Publisher_xml | – name: Blackwell Publishing Ltd – name: Wiley Subscription Services, Inc |
| References | Fan XL, Deng SG. Remarks on Ricceri's variational principle and applications to the p(x)-Laplacian equations. Nonlinear Analysis 2007; 67:3064-3075. Bonanno G, Candito P. Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities. Journal of Differential Equations 2008; 244:3031-3059. Bonanno G, Chinnì A. Existence results of infinitely many solutions for p(x)-Laplacian elliptic Dirichlet problems. Complex Variables and Elliptic Equations 2012; 57:1233-1246. Bonanno G, Chinnì A. Discontinuous elliptic problems involving the p(x)-Laplacian. Mathematische Nachrichten 2011; 284:639-652. Kristály A, Rădulescu V, Varga C. Variational Principles in Mathematical Physics, Geometry, and Economics: Qualitative Analysis of Nonlinear Equations and Unilateral Problems, Encyclopedia of Mathematics and its Applications, Vol. 136. Cambridge University Press: Cambridge, 2010. D'Aguì G, Heidarkhani S, Molica Bisci G. Multiple solutions for a perturbed mixed boundary value problem involving the one-dimensional p-Laplacian. Electronic Journal of Qualitative Theory of Differential Equations 2013; 24:1-14. Bonanno G, Marano SA. On the structure of the critical set of non-differentiable functions with a weak compactness condition. Applied Analysis 2010; 89:1-10. Chen Y, Levine S, Rao M. Variable exponent linear growth functional in image restoration. SIAM Journal on Applied Mathematics 2006; 66(4):1383-1406. Antontsev SN, Shmarev SI. A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions. Nonlinear Analysis 2005; 60:515-545. Ricceri B. A general variational principle and some of its applications. Journal of Computational and Applied Mathematics 2000; 113:401-410. D'Aguì G, Sciammetta A. Infinitely many solutions to elliptic problems with variable exponent and nonhomogeneous Neumann conditions. Nonlinear Analysis 2012; 75:5612-5619. Allaoui M, El Amrouss AR, Ourraoui A. Existence and multiplicity of solutions for a Steklov problem involving the p(x)-Laplace operator. Electronic Journal of Differential Equations 2012; 132:1-12. Bonanno G, Molica Bisci G. Infinitely many solutions for a boundary value problem with discontinuous nonlinearities. Boundary Value Problems 2009; 2009:1-20. Ruz̆ic̆ka M. Electro-rheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Math., vol. 1784. Springer-Verlag: Berlin, 2000. Cammaroto F, Chinnì A, Di Bella B. Multiple solutions for a Neumann problem involving the p(x)-Laplacian. Nonlinear Analysis 2009; 71:4486-4492. Bonanno G, Chinnì A. Existence of three solutions for a perturbed two-point boundary value problem. Applied Mathematics Letters 2010; 23:807-811. Fan XL, Zhao D. On the spaces Lp(x)(Ω) and Wm,p(x)(Ω). Journal of Mathematical Analysis and Applications 2001; 263:424-446. Ji C. Remarks on the existence of three solutions for the p(x)-Laplacian equations. Nonlinear Analysis 2011; 74:2908-2915. Chinnì A, Livrea R. Multiple solutions for a Neumann-type differential inclusion problem involving the p(.)-Laplacian. Discrete and Continuous Dynamical Systems-Series S (DCDS-S) 2012; 5:753-764. Bonanno G, Chinnì A. Multiple solutions for elliptic problems involving the p(x)-Laplacian. Matematiche (Catania) 2011; 66:105-113. Bonanno G, D'Aguì G. Multiplicity results for a perturbed elliptic Neumann problem. Abstract and Applied Analysis 2010; 1-10. Zhikov VV. Averaging of functionals of the calculus of variations and elasticity theory. Mathematics of the USSR-Izvestiya 1987; 29:33-66. Bonanno G, Di Bella B, Henderson J. Existence of solutions to second-order boundary-value problems with small perturbations of impulses. Electronic Journal of Differential Equations 2013; 126:1-14. Antontsev SN, Rodrigues JF. On stationary thermo-rheological viscous flows. Annali dell'Universitá di Ferrara. Sezione VII. Scienze Matematiche 2006; 52:19-36. Dai G. Infinitely many non-negative solutions for a Dirichlet problem involving p(x)-Laplacian. Nonlinear Analysis 2009; 71:5840-5849. Fan XL, Shen JS, Zhao D. Sobolev embedding theorems for spaces Wk,p(x)(Ω). Journal of Mathematical Analysis and Applications 2001; 262:749-760. Yin H. Existence of three solutions for a Neumann problem involving the p(x)-Laplace operator. Mathematical Methods in the Applied Sciences 2012; 35:307-313. Harjulehto P, Hästö P, Latvala V. Minimizers of the variable exponent, non-uniformly convex Dirichlet energy. Journal de Mathématiques Pures et Appliquées 2008; 89:174-197. Kovác̆ik O, Rákosník J. On spaces Lp(x) and Wk,p(x). Czechoslovak Mathematical Journal 1991; 41:592-618. Candito P, D'Aguì G. Three solutions to a perturbed nonlinear discrete Dirichlet problem. Journal of Mathematical Analysis and Applications 2011; 375:594-601. 2006; 52 2001; 263 2001; 262 2000; 113 2010 2013; 24 2013; 126 2011; 74 2005; 60 2008; 244 2012; 57 2012; 35 2012; 75 2011; 375 2010; 89 2010; 23 2009; 2009 2012; 132 2000 2006; 66 2009; 71 1991; 41 2008; 89 2011; 66 2011; 284 2012; 5 2007; 67 1987; 29 Bonanno G (e_1_2_4_30_1) 2013; 126 Bonanno G (e_1_2_4_29_1) 2010 e_1_2_4_21_1 e_1_2_4_20_1 e_1_2_4_23_1 e_1_2_4_22_1 e_1_2_4_25_1 e_1_2_4_24_1 e_1_2_4_27_1 e_1_2_4_26_1 e_1_2_4_28_1 e_1_2_4_3_1 Antontsev SN (e_1_2_4_7_1) 2005; 60 Allaoui M (e_1_2_4_10_1) 2012; 132 e_1_2_4_2_1 e_1_2_4_5_1 e_1_2_4_4_1 e_1_2_4_6_1 e_1_2_4_8_1 Kovác̆ik O (e_1_2_4_9_1) 1991; 41 e_1_2_4_32_1 e_1_2_4_31_1 e_1_2_4_12_1 e_1_2_4_13_1 e_1_2_4_15_1 e_1_2_4_16_1 e_1_2_4_18_1 e_1_2_4_17_1 Chinnì A (e_1_2_4_14_1) 2012; 5 e_1_2_4_19_1 Bonanno G (e_1_2_4_11_1) 2011; 66 |
| References_xml | – reference: Harjulehto P, Hästö P, Latvala V. Minimizers of the variable exponent, non-uniformly convex Dirichlet energy. Journal de Mathématiques Pures et Appliquées 2008; 89:174-197. – reference: Bonanno G, Molica Bisci G. Infinitely many solutions for a boundary value problem with discontinuous nonlinearities. Boundary Value Problems 2009; 2009:1-20. – reference: Bonanno G, Chinnì A. Discontinuous elliptic problems involving the p(x)-Laplacian. Mathematische Nachrichten 2011; 284:639-652. – reference: Kristály A, Rădulescu V, Varga C. Variational Principles in Mathematical Physics, Geometry, and Economics: Qualitative Analysis of Nonlinear Equations and Unilateral Problems, Encyclopedia of Mathematics and its Applications, Vol. 136. Cambridge University Press: Cambridge, 2010. – reference: Dai G. Infinitely many non-negative solutions for a Dirichlet problem involving p(x)-Laplacian. Nonlinear Analysis 2009; 71:5840-5849. – reference: Bonanno G, Chinnì A. Existence of three solutions for a perturbed two-point boundary value problem. Applied Mathematics Letters 2010; 23:807-811. – reference: Fan XL, Shen JS, Zhao D. Sobolev embedding theorems for spaces Wk,p(x)(Ω). Journal of Mathematical Analysis and Applications 2001; 262:749-760. – reference: Antontsev SN, Shmarev SI. A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions. Nonlinear Analysis 2005; 60:515-545. – reference: Ricceri B. A general variational principle and some of its applications. Journal of Computational and Applied Mathematics 2000; 113:401-410. – reference: Bonanno G, Chinnì A. Multiple solutions for elliptic problems involving the p(x)-Laplacian. Matematiche (Catania) 2011; 66:105-113. – reference: Chinnì A, Livrea R. Multiple solutions for a Neumann-type differential inclusion problem involving the p(.)-Laplacian. Discrete and Continuous Dynamical Systems-Series S (DCDS-S) 2012; 5:753-764. – reference: Yin H. Existence of three solutions for a Neumann problem involving the p(x)-Laplace operator. Mathematical Methods in the Applied Sciences 2012; 35:307-313. – reference: Fan XL, Zhao D. On the spaces Lp(x)(Ω) and Wm,p(x)(Ω). Journal of Mathematical Analysis and Applications 2001; 263:424-446. – reference: Bonanno G, Candito P. Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities. Journal of Differential Equations 2008; 244:3031-3059. – reference: D'Aguì G, Heidarkhani S, Molica Bisci G. Multiple solutions for a perturbed mixed boundary value problem involving the one-dimensional p-Laplacian. Electronic Journal of Qualitative Theory of Differential Equations 2013; 24:1-14. – reference: Bonanno G, D'Aguì G. Multiplicity results for a perturbed elliptic Neumann problem. Abstract and Applied Analysis 2010; 1-10. – reference: Ji C. Remarks on the existence of three solutions for the p(x)-Laplacian equations. Nonlinear Analysis 2011; 74:2908-2915. – reference: D'Aguì G, Sciammetta A. Infinitely many solutions to elliptic problems with variable exponent and nonhomogeneous Neumann conditions. Nonlinear Analysis 2012; 75:5612-5619. – reference: Fan XL, Deng SG. Remarks on Ricceri's variational principle and applications to the p(x)-Laplacian equations. Nonlinear Analysis 2007; 67:3064-3075. – reference: Bonanno G, Marano SA. On the structure of the critical set of non-differentiable functions with a weak compactness condition. Applied Analysis 2010; 89:1-10. – reference: Cammaroto F, Chinnì A, Di Bella B. Multiple solutions for a Neumann problem involving the p(x)-Laplacian. Nonlinear Analysis 2009; 71:4486-4492. – reference: Zhikov VV. Averaging of functionals of the calculus of variations and elasticity theory. Mathematics of the USSR-Izvestiya 1987; 29:33-66. – reference: Kovác̆ik O, Rákosník J. On spaces Lp(x) and Wk,p(x). Czechoslovak Mathematical Journal 1991; 41:592-618. – reference: Bonanno G, Di Bella B, Henderson J. Existence of solutions to second-order boundary-value problems with small perturbations of impulses. Electronic Journal of Differential Equations 2013; 126:1-14. – reference: Ruz̆ic̆ka M. Electro-rheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Math., vol. 1784. Springer-Verlag: Berlin, 2000. – reference: Bonanno G, Chinnì A. Existence results of infinitely many solutions for p(x)-Laplacian elliptic Dirichlet problems. Complex Variables and Elliptic Equations 2012; 57:1233-1246. – reference: Allaoui M, El Amrouss AR, Ourraoui A. Existence and multiplicity of solutions for a Steklov problem involving the p(x)-Laplace operator. Electronic Journal of Differential Equations 2012; 132:1-12. – reference: Antontsev SN, Rodrigues JF. On stationary thermo-rheological viscous flows. Annali dell'Universitá di Ferrara. Sezione VII. Scienze Matematiche 2006; 52:19-36. – reference: Chen Y, Levine S, Rao M. Variable exponent linear growth functional in image restoration. SIAM Journal on Applied Mathematics 2006; 66(4):1383-1406. – reference: Candito P, D'Aguì G. Three solutions to a perturbed nonlinear discrete Dirichlet problem. Journal of Mathematical Analysis and Applications 2011; 375:594-601. – volume: 132 start-page: 1 year: 2012 end-page: 12 article-title: Existence and multiplicity of solutions for a Steklov problem involving the ( )‐Laplace operator publication-title: Electronic Journal of Differential Equations – volume: 284 start-page: 639 year: 2011 end-page: 652 article-title: Discontinuous elliptic problems involving the ( )‐Laplacian publication-title: Mathematische Nachrichten – volume: 126 start-page: 1 year: 2013 end-page: 14 article-title: Existence of solutions to second‐order boundary‐value problems with small perturbations of impulses publication-title: Electronic Journal of Differential Equations – volume: 29 start-page: 33 year: 1987 end-page: 66 article-title: Averaging of functionals of the calculus of variations and elasticity theory publication-title: Mathematics of the USSR‐Izvestiya – volume: 67 start-page: 3064 year: 2007 end-page: 3075 article-title: Remarks on Ricceri's variational principle and applications to the ( )‐Laplacian equations publication-title: Nonlinear Analysis – volume: 5 start-page: 753 year: 2012 end-page: 764 article-title: Multiple solutions for a Neumann‐type differential inclusion problem involving the (.)‐Laplacian publication-title: Discrete and Continuous Dynamical Systems‐Series S (DCDS‐S) – volume: 113 start-page: 401 year: 2000 end-page: 410 article-title: A general variational principle and some of its applications publication-title: Journal of Computational and Applied Mathematics – start-page: 1 year: 2010 end-page: 10 article-title: Multiplicity results for a perturbed elliptic Neumann problem publication-title: Abstract and Applied Analysis – volume: 57 start-page: 1233 year: 2012 end-page: 1246 article-title: Existence results of infinitely many solutions for ( )‐Laplacian elliptic Dirichlet problems publication-title: Complex Variables and Elliptic Equations – volume: 71 start-page: 4486 year: 2009 end-page: 4492 article-title: Multiple solutions for a Neumann problem involving the ( )‐Laplacian publication-title: Nonlinear Analysis – year: 2000 – volume: 244 start-page: 3031 year: 2008 end-page: 3059 article-title: Non‐differentiable functionals and applications to elliptic problems with discontinuous nonlinearities publication-title: Journal of Differential Equations – volume: 35 start-page: 307 year: 2012 end-page: 313 article-title: Existence of three solutions for a Neumann problem involving the ( )‐Laplace operator publication-title: Mathematical Methods in the Applied Sciences – volume: 52 start-page: 19 year: 2006 end-page: 36 article-title: On stationary thermo‐rheological viscous flows publication-title: Annali dell'Universitá di Ferrara. Sezione VII. Scienze Matematiche – volume: 74 start-page: 2908 year: 2011 end-page: 2915 article-title: Remarks on the existence of three solutions for the ( )‐Laplacian equations publication-title: Nonlinear Analysis – year: 2010 – volume: 60 start-page: 515 year: 2005 end-page: 545 article-title: A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions publication-title: Nonlinear Analysis – volume: 41 start-page: 592 year: 1991 end-page: 618 article-title: On spaces and publication-title: Czechoslovak Mathematical Journal – volume: 75 start-page: 5612 year: 2012 end-page: 5619 article-title: Infinitely many solutions to elliptic problems with variable exponent and nonhomogeneous Neumann conditions publication-title: Nonlinear Analysis – volume: 263 start-page: 424 year: 2001 end-page: 446 article-title: On the spaces (Ω) and (Ω) publication-title: Journal of Mathematical Analysis and Applications – volume: 66 start-page: 105 year: 2011 end-page: 113 article-title: Multiple solutions for elliptic problems involving the ( )‐Laplacian publication-title: Matematiche (Catania) – volume: 66 start-page: 1383 issue: 4 year: 2006 end-page: 1406 article-title: Variable exponent linear growth functional in image restoration publication-title: SIAM Journal on Applied Mathematics – volume: 24 start-page: 1 year: 2013 end-page: 14 article-title: Multiple solutions for a perturbed mixed boundary value problem involving the one‐dimensional ‐Laplacian publication-title: Electronic Journal of Qualitative Theory of Differential Equations – volume: 89 start-page: 174 year: 2008 end-page: 197 article-title: Minimizers of the variable exponent, non‐uniformly convex Dirichlet energy publication-title: Journal de Mathématiques Pures et Appliquées – volume: 262 start-page: 749 year: 2001 end-page: 760 article-title: Sobolev embedding theorems for spaces (Ω) publication-title: Journal of Mathematical Analysis and Applications – volume: 89 start-page: 1 year: 2010 end-page: 10 article-title: On the structure of the critical set of non‐differentiable functions with a weak compactness condition publication-title: Applied Analysis – volume: 375 start-page: 594 year: 2011 end-page: 601 article-title: Three solutions to a perturbed nonlinear discrete Dirichlet problem publication-title: Journal of Mathematical Analysis and Applications – volume: 23 start-page: 807 year: 2010 end-page: 811 article-title: Existence of three solutions for a perturbed two‐point boundary value problem publication-title: Applied Mathematics Letters – volume: 71 start-page: 5840 year: 2009 end-page: 5849 article-title: Infinitely many non‐negative solutions for a Dirichlet problem involving ( )‐Laplacian publication-title: Nonlinear Analysis – volume: 2009 start-page: 1 year: 2009 end-page: 20 article-title: Infinitely many solutions for a boundary value problem with discontinuous nonlinearities publication-title: Boundary Value Problems – volume: 41 start-page: 592 year: 1991 ident: e_1_2_4_9_1 article-title: On spaces L p(x) and W k,p(x) publication-title: Czechoslovak Mathematical Journal doi: 10.21136/CMJ.1991.102493 – ident: e_1_2_4_19_1 doi: 10.1016/j.na.2010.12.013 – ident: e_1_2_4_5_1 doi: 10.1016/j.matpur.2007.10.006 – ident: e_1_2_4_13_1 doi: 10.1016/j.na.2009.03.009 – volume: 5 start-page: 753 year: 2012 ident: e_1_2_4_14_1 article-title: Multiple solutions for a Neumann‐type differential inclusion problem involving the p(.)‐Laplacian publication-title: Discrete and Continuous Dynamical Systems‐Series S (DCDS‐S) doi: 10.3934/dcdss.2012.5.753 – volume: 132 start-page: 1 year: 2012 ident: e_1_2_4_10_1 article-title: Existence and multiplicity of solutions for a Steklov problem involving the p(x)‐Laplace operator publication-title: Electronic Journal of Differential Equations – ident: e_1_2_4_18_1 doi: 10.1016/j.matpur.2007.10.006 – ident: e_1_2_4_6_1 doi: 10.1007/s11565-006-0002-9 – ident: e_1_2_4_16_1 doi: 10.1016/j.na.2012.05.009 – volume: 60 start-page: 515 year: 2005 ident: e_1_2_4_7_1 article-title: A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions publication-title: Nonlinear Analysis doi: 10.1016/j.na.2004.09.026 – ident: e_1_2_4_8_1 doi: 10.1006/jmaa.2000.7617 – ident: e_1_2_4_22_1 doi: 10.1016/S0377-0427(99)00269-1 – volume: 66 start-page: 105 year: 2011 ident: e_1_2_4_11_1 article-title: Multiple solutions for elliptic problems involving the p(x)‐Laplacian publication-title: Matematiche (Catania) – ident: e_1_2_4_15_1 doi: 10.1016/j.na.2009.05.007 – volume: 126 start-page: 1 year: 2013 ident: e_1_2_4_30_1 article-title: Existence of solutions to second‐order boundary‐value problems with small perturbations of impulses publication-title: Electronic Journal of Differential Equations – ident: e_1_2_4_2_1 doi: 10.1007/BFb0104029 – ident: e_1_2_4_26_1 doi: 10.1006/jmaa.2001.7618 – ident: e_1_2_4_23_1 doi: 10.1155/2009/670675 – ident: e_1_2_4_25_1 doi: 10.1016/j.jde.2008.02.025 – ident: e_1_2_4_17_1 doi: 10.1016/j.na.2006.09.060 – ident: e_1_2_4_3_1 doi: 10.1070/IM1987v029n01ABEH000958 – ident: e_1_2_4_31_1 doi: 10.1016/j.jmaa.2010.09.050 – ident: e_1_2_4_27_1 doi: 10.1017/CBO9780511760631 – ident: e_1_2_4_32_1 doi: 10.14232/ejqtde.2013.1.24 – ident: e_1_2_4_12_1 doi: 10.1080/17476933.2012.662225 – ident: e_1_2_4_24_1 doi: 10.1080/00036810903397438 – ident: e_1_2_4_28_1 doi: 10.1016/j.aml.2010.03.015 – start-page: 1 year: 2010 ident: e_1_2_4_29_1 article-title: Multiplicity results for a perturbed elliptic Neumann problem publication-title: Abstract and Applied Analysis doi: 10.1155/2010/564363 – ident: e_1_2_4_4_1 doi: 10.1137/050624522 – ident: e_1_2_4_21_1 doi: 10.1002/mana.200810232 – ident: e_1_2_4_20_1 doi: 10.1002/mma.1568 |
| SSID | ssj0008112 |
| Score | 2.0778496 |
| Snippet | Applying three critical point theorems, we prove the existence of at least three weak solutions for a class of differential equations with p(x)‐Laplacian and... Applying three critical point theorems, we prove the existence of at least three weak solutions for a class of differential equations with p ( x )‐Laplacian... Applying three critical point theorems, we prove the existence of at least three weak solutions for a class of differential equations with p(x)-Laplacian and... |
| SourceID | proquest crossref wiley istex |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 2589 |
| SubjectTerms | Critical point Differential equations Existence theorems Exponents Mathematical analysis multiple solutions Neumann problem p(x)-Laplacian Perturbation methods Theorems variable exponent Sobolev spaces |
| Title | Multiplicity results for elliptic problems with variable exponent and nonhomogeneous Neumann conditions |
| URI | https://api.istex.fr/ark:/67375/WNG-24RDCQNL-B/fulltext.pdf https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fmma.3244 https://www.proquest.com/docview/1696054867 https://www.proquest.com/docview/1718953317 |
| Volume | 38 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1ba9VAEF6kvuiDtlXxtLWsIFUfcppNZnN5rL1YxBywWCz4sOwtWupJSnOOFH-9M7nVioL4FEImbDI7s_PN7uy3jL1wBjFrAjKwrpQBJNoFOZgogNJgj0MZJoY2Chez5PgU3p3Js76qkvbCdPwQ44QbeUY7XpODa9Ps3pCGzud6imiAqEBFnBBt_sHJDXNUJtqFTmKHCSASMPDOhtHu8OKtSHSXlHp9C2b-ClbbaHP0kH0evrMrMrmYLhdman_8RuH4fz-yyh70IJTvdVazxu74ap3dL0YG12adrfVO3_BXPTP160fsS9GVH55bxO4cE3W8bTjCXk60njj4WN4fUNNwmuDl3zETp71Z3F9f1hXGN64rx6u6-lrPazRdXy8bPvO0kFBxzMxdV0D2mJ0eHX7cPw76kxoCCzFAAD7UBrNdWQqnPWbcNpQml87npS_LLC21ts7kkOUedKqtiXIcKzIX5iHEOpHxE7aCbfunjAtII-Igy0CUkBib5QZTWJdSZml0LCbs5dBryvY05nSaxjfVETBHCvWpSJ8T9nyUvOyoO_4gs9N2_Cigry6o1C2V6tPsrYrg5GD_w-y9ejNhW4NlqN7LGyUSzP8kcRZiW-Nj9E9adNGtDpXA4E8lvAJldloz-OvHqKLYo-vGvwpusnuI32RXj7jFVhZXS_8MMdLCbLfe8BPUnQ8A |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9QwELZKewAOQAuIhQJGQgUO2SbZcR7iVAplgU0kqlbtAcnyK4DKJlWziyp-PTN5lSKQEKcoykROxh7PN57xZ8aeWo2YNQLhGVsIDyJlvRR06EGhsceh8CNNG4WzPJoewvtjcbzCXvZ7YVp-iGHBjSyjma_JwGlBevuCNXQ-V2OEA3CFrTXpOUJE-xfcUUnQpDqJH8aDMICeedYPt_s3L_miNVLr-SWg-StcbfzN3k32qf_StszkZLxc6LH58RuJ43_-yi12o8OhfKcdOOtsxZUb7Ho2kLjWG2y9s_uaP-_IqV_cZp-ztgLxq0H4zjFWx9uaI_LlxOyJ84_h3Rk1Nac1Xv4dg3HansXd-WlVoovjqrS8rMov1bzC0euqZc1zR7mEkmNwbtsasjvscO_Nwe7U6w5r8AxMADxwvtIY8IoisMph0G18oVNhXVq4okjiQiljdQpJ6kDFyugwxekisX7qw0RFYnKXrWLb7h7jAcQh0ZAlEBQQaZOkGqNYG1NwqdUkGLFnfbdJ0zGZ04Ea32TLwRxK1KckfY7Yk0HytGXv-IPMVtPzg4A6O6Fqt1jIo_ytDGH_9e7HfCZfjdhmPzRkZ-i1DCIMAQXRFmJbw2M0Ucq7qEaHMkD_T1W8AcpsNePgrx8js2yHrvf_VfAxuzo9yGZy9i7_8IBdQzgn2vLETba6OFu6hwiZFvpRYxo_AbWoEx4 |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9QwELaglRA9AC0gFgoYCRU4ZJtkx3kcS8tSoImgoqISB8uO7YLKJqtmF1X8embyKkUgIU5RlImcjGc839jjz4w9NRoxawTCK4wTHkTKeCno0AOnscfB-ZGmjcJZHu0fwdtjcdxVVdJemJYfYphwI89oxmty8Llx2xekobOZGiMagKtsFSKMkgSIDi-oo5KgWekkehgPwgB64lk_3O7fvBSKVkmr55dw5q9otQk305vsc_-hbZXJ6Xi50OPix28cjv_3J7fYjQ6F8p3WbNbZFVtusLVsoHCtN9h65_U1f95RU7-4zU6ytv7wa4HgnWOmjrc1R9zLidcTR5-CdyfU1JxmePl3TMVpcxa35_OqxADHVWl4WZVfqlmFtmurZc1zSysJJcfU3LQVZHfY0fTVx919rzuqwStgAuCB9ZXGdFe4wCiLKXfhC50KY1NnnUtip1RhdApJakHFqtBhioNFYvzUh4mKxOQuW8G27T3GA4hDIiFLIHAQ6SJJNeawJqbUUqtJMGLP-l6TRcdjTsdpfJMtA3MoUZ-S9DliTwbJecvd8QeZrabjBwF1dkq1brGQn_LXMoTDvd0P-YF8OWKbvWXIzs1rGUSYAAoiLcS2hsfooLTqohodygCjP9XwBiiz1ZjBXz9GZtkOXe__q-Bjdu393lQevMnfPWDXEcuJtjZxk60szpb2IeKlhX7UOMZPdrwRzQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Multiplicity+results+for+elliptic+problems+with+variable+exponent+and+nonhomogeneous+Neumann+conditions&rft.jtitle=Mathematical+methods+in+the+applied+sciences&rft.au=Heidarkhani%2C+Shapour&rft.au=Afrouzi%2C+Ghasem+A.&rft.au=Hadjian%2C+Armin&rft.date=2015-08-01&rft.issn=0170-4214&rft.eissn=1099-1476&rft.volume=38&rft.issue=12&rft.spage=2589&rft.epage=2599&rft_id=info:doi/10.1002%2Fmma.3244&rft.externalDBID=10.1002%252Fmma.3244&rft.externalDocID=MMA3244 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0170-4214&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0170-4214&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0170-4214&client=summon |