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arXiv · 1901.06197

Asymmetric Robin problems with indefinite potential and concave terms

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

We consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential. In the reaction, we have the competing effects of a concave term appearing with a negative sign and of an asymmetric asymptotically linear term which is resonant in the negative direction. Using variational methods together with truncation and perturbation techniques and Morse theory (critical groups) we prove two multiplicity theorems producing four and five respectively nontrivial smooth solutions when the parameter $\lambda>0$ is small.

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Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. 2019-01-18. Asymmetric Robin problems with indefinite potential and concave terms. https://doi.org/10.1515/ans-2018-2022 10.1515/ans-2018-2022

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