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arXiv · 1911.01781

Parametric nonlinear resonant Robin problems

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

We consider a nonlinear Robin problem driven by the $p$-Laplacian. In the reaction we have the competing effects of two nonlinearities. One term is parametric, strictly $(p-1)$-sublinear and the other one is $(p-1)$-linear and resonant at any nonprincipal variational eigenvalue. Using variational tools from the critical theory (critical groups), we show that for all large enough values of parameter $\lambda$ the problem has at least five nontrivial smooth solutions.

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Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. 2019-11-05. Parametric nonlinear resonant Robin problems. https://doi.org/10.1002/mana.201800505

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