Multiple solutions with sign information for superlinear (p, q)-equations

We consider a nonlinear Dirichlet problem driven by the ( p ,  q )-Laplacian and with a Carathéodory reaction f ( z ,  x ) which is ( p - 1 )-superlinear in x ∈ R but without satisfying the Ambrosetti–Rabinowitz condition. Using variational tools and critical groups, we prove a multiplicity theorem...

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Published inPositivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 25; no. 5; pp. 1805 - 1820
Main Authors Liu, Zhenhai, Papageorgiou, Nikolaos S.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.11.2021
Springer Nature B.V
Subjects
Banach spaces
Calculus of Variations and Optimal Control; Optimization
Dirichlet problem
Econometrics
Eigenvalues
Fourier Analysis
Laboratories
Mathematics
Mathematics and Statistics
Operator Theory
Potential Theory
35J20
58E05
critical groups
35J60
49H20
(
Constant sign and nodal solutions
Nonlinear regularity
Superlinear reaction
,
Laplacian
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ISSN1385-1292
1572-9281
DOI10.1007/s11117-021-00839-0

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Summary:We consider a nonlinear Dirichlet problem driven by the ( p ,  q )-Laplacian and with a Carathéodory reaction f ( z ,  x ) which is ( p - 1 )-superlinear in x ∈ R but without satisfying the Ambrosetti–Rabinowitz condition. Using variational tools and critical groups, we prove a multiplicity theorem producing three nontrivial smooth solutions all with sign information (one positive, one negative and one nodal).
Bibliography:ObjectType-Article-1
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ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-021-00839-0