Eigenvalue criteria for the existence of multiple positive solutions of high-order nonlinear BVPs
The existence of multiple positive solutions for the integral equation u ( t ) = ∫ 0 1 g ( t , s ) h ( s ) f ( s , A n − 1 u ( s ) , … , A 1 u ( s ) , u ( s ) ) d s is studied by using eigenvalue criteria. Using these results we obtain new results on the existence of multiple positive solutions for...
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| Published in | Nonlinear analysis Vol. 69; no. 1; pp. 295 - 303 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier Ltd
01.07.2008
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0362-546X 1873-5215 |
| DOI | 10.1016/j.na.2007.05.020 |
Cover
| Abstract | The existence of multiple positive solutions for the integral equation
u
(
t
)
=
∫
0
1
g
(
t
,
s
)
h
(
s
)
f
(
s
,
A
n
−
1
u
(
s
)
,
…
,
A
1
u
(
s
)
,
u
(
s
)
)
d
s
is studied by using eigenvalue criteria. Using these results we obtain new results on the existence of multiple positive solutions for high-order nonlinear differential equations, subject to local and nonlocal boundary conditions. |
|---|---|
| AbstractList | The existence of multiple positive solutions for the integral equation
u
(
t
)
=
∫
0
1
g
(
t
,
s
)
h
(
s
)
f
(
s
,
A
n
−
1
u
(
s
)
,
…
,
A
1
u
(
s
)
,
u
(
s
)
)
d
s
is studied by using eigenvalue criteria. Using these results we obtain new results on the existence of multiple positive solutions for high-order nonlinear differential equations, subject to local and nonlocal boundary conditions. The existence of multiple positive solutions for the integral equation is studied by using eigenvalue criteria. Using these results we obtain new results on the existence of multiple positive solutions for high-order nonlinear differential equations, subject to local and nonlocal boundary conditions. |
| Author | Jiang, Weihua |
| Author_xml | – sequence: 1 givenname: Weihua surname: Jiang fullname: Jiang, Weihua email: weihuajiang@hebust.edu.cn organization: College of Mathematics and Science of Information, Hebei Normal University, Shijiazhuang, 050016, Hebei, PR China |
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| Cites_doi | 10.1016/j.aml.2004.05.009 10.1006/jmaa.2000.7028 10.1006/jmaa.1999.6500 10.1016/j.jmaa.2003.08.038 |
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| Keywords | 34B15 Green’s function Eigenvalue criteria 34B10 m -point boundary value problem Green's function; Eigenvalue criteria; m-point boundary value problem Boundary value problem Existence of solution Nonlinear analysis Eigenvalue 34B10; 34B15 Mathematical model Green function |
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| References | Eloe, Henderson (b2) 1995; 03 Guo, Liu, Qiu (b5) 2004; 289 Davis, Eloe, Henderson (b4) 1999; 237 Nussbaum (b7) 1981 th order differential equation with Lidstone boundary conditions, Ph.D. Dissertation, Auburn University, 1997 Guo, Lakshmikantham (b8) 1988 Davis, Henderson, Wong (b3) 2000; 251 T.M. Lamar, Analysis of a Eloe, Ahmad (b1) 2005; 18 Guo (10.1016/j.na.2007.05.020_b5) 2004; 289 Eloe (10.1016/j.na.2007.05.020_b1) 2005; 18 Davis (10.1016/j.na.2007.05.020_b3) 2000; 251 10.1016/j.na.2007.05.020_b6 Nussbaum (10.1016/j.na.2007.05.020_b7) 1981 Guo (10.1016/j.na.2007.05.020_b8) 1988 Eloe (10.1016/j.na.2007.05.020_b2) 1995; 03 Davis (10.1016/j.na.2007.05.020_b4) 1999; 237 |
| References_xml | – volume: 251 start-page: 527 year: 2000 end-page: 548 ident: b3 article-title: General Lidstone problem: Multiplicity and symmetry of solutions publication-title: J. Math. Anal. Appl. – volume: 18 start-page: 521 year: 2005 end-page: 527 ident: b1 article-title: Positive solutions of a nonlinear publication-title: Appl. Math. Lett. – start-page: 309 year: 1981 end-page: 330 ident: b7 article-title: Eigenvectors of nonlinear positive operators and the linear Krein–Rutman theorem publication-title: Fixed Point Theory, in: Lecture Notes in Math. vol. 886 – reference: th order differential equation with Lidstone boundary conditions, Ph.D. Dissertation, Auburn University, 1997 – volume: 03 start-page: 1 year: 1995 end-page: 8 ident: b2 article-title: Positive solutions for higher order ordinary differential equations publication-title: Electron. J. Differential Equations – year: 1988 ident: b8 article-title: Nonlinear Problem in Abstract Cones – volume: 289 start-page: 545 year: 2004 end-page: 553 ident: b5 article-title: Three positive solutions for higher order m-point boundary value problems publication-title: J. Math. Anal. Appl. – volume: 237 start-page: 710 year: 1999 end-page: 720 ident: b4 article-title: Triple positive solutions and dependence on higher order derivatives publication-title: J. Math. Anal. Appl. – reference: T.M. Lamar, Analysis of a – volume: 18 start-page: 521 year: 2005 ident: 10.1016/j.na.2007.05.020_b1 article-title: Positive solutions of a nonlinear nth order boundary value problem with nonlocal conditions publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2004.05.009 – volume: 251 start-page: 527 year: 2000 ident: 10.1016/j.na.2007.05.020_b3 article-title: General Lidstone problem: Multiplicity and symmetry of solutions publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.2000.7028 – year: 1988 ident: 10.1016/j.na.2007.05.020_b8 – volume: 237 start-page: 710 year: 1999 ident: 10.1016/j.na.2007.05.020_b4 article-title: Triple positive solutions and dependence on higher order derivatives publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.1999.6500 – start-page: 309 year: 1981 ident: 10.1016/j.na.2007.05.020_b7 article-title: Eigenvectors of nonlinear positive operators and the linear Krein–Rutman theorem – volume: 03 start-page: 1 year: 1995 ident: 10.1016/j.na.2007.05.020_b2 article-title: Positive solutions for higher order ordinary differential equations publication-title: Electron. J. Differential Equations – volume: 289 start-page: 545 year: 2004 ident: 10.1016/j.na.2007.05.020_b5 article-title: Three positive solutions for higher order m-point boundary value problems publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2003.08.038 – ident: 10.1016/j.na.2007.05.020_b6 |
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| Snippet | The existence of multiple positive solutions for the integral equation
u
(
t
)
=
∫
0
1
g
(
t
,
s
)
h
(
s
)
f
(
s
,
A
n
−
1
u
(
s
)
,
…
,
A
1
u
(
s
)
,
u
(
s
)... The existence of multiple positive solutions for the integral equation is studied by using eigenvalue criteria. Using these results we obtain new results on... |
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| SubjectTerms | 34B10 34B15 [formula omitted]-point boundary value problem Eigenvalue criteria Exact sciences and technology Green’s function Mathematical analysis Mathematics Nonlinear algebraic and transcendental equations Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Ordinary differential equations Partial differential equations, boundary value problems Sciences and techniques of general use |
| Title | Eigenvalue criteria for the existence of multiple positive solutions of high-order nonlinear BVPs |
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