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arXiv · 2006.01454

Existence and multiplicity of solutions for double-phase Robin problems

Nikolaos S. Papageorgiou·Vicenţiu D. Rădulescu·Dušan D. Repovš
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Abstract

We consider a double phase Robin problem with a Carath\'{e}odory nonlinearity. When the reaction is superlinear but without satisfying the Ambrosetti-Rabinowitz condition, we prove an existence theorem. When the reaction is resonant, we prove a multiplicity theorem. Our approach is Morse theoretic, using the notion of homological local linking.

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Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. 2020-06-02. Existence and multiplicity of solutions for double-phase Robin problems. https://doi.org/10.1112/blms.12347

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