Resonant double phase equations

We consider a double phase Dirichlet equation with a reaction which is asymptotically as x→±∞, resonant with respect to the first eigenvalue of a related eigenvalue problem. Using variational tools together with Morse theoretic arguments, we prove the existence of at least two bounded nontrivial sol...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 64; p. 103454
Main Authors Papageorgiou, Nikolaos S., Rădulescu, Vicenţiu D., Zhang, Youpei
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2022
Subjects
Critical groups
Double phase equation
Maximum principle
Musielak–Orlicz–Sobolev spaces
Resonance
Unbalanced growth
Double phase equation
Maximum principle
Resonance
Musielak–Orlicz–Sobolev spaces
Critical groups
Unbalanced growth
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Summary:We consider a double phase Dirichlet equation with a reaction which is asymptotically as x→±∞, resonant with respect to the first eigenvalue of a related eigenvalue problem. Using variational tools together with Morse theoretic arguments, we prove the existence of at least two bounded nontrivial solutions for the problem.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2021.103454