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arXiv · 1804.10003

Positive solutions for nonlinear nonhomogeneous parametric Robin problems

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

We study a parametric Robin problem driven by a nonlinear nonhomogeneous differential operator and with a superlinear Carathéodory reaction term. We prove a bifurcation-type theorem for small values of the parameter. Also, we show that as the parameter $λ>0$ approaches zero we can find positive solutions with arbitrarily big and arbitrarily small Sobolev norm. Finally we show that for every admissible parameter value there is a smallest positive solution $u^*_λ$ of the problem and we investigate the properties of the map $λ\mapsto u^*_λ$.

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Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. 2018-04-26. Positive solutions for nonlinear nonhomogeneous parametric Robin problems. https://doi.org/10.1515/forum-2017-0124

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