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arXiv · 2010.03846

Positive solutions for the Robin $p$-Laplacian plus an indefinite potential

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

We consider a nonlinear elliptic equation driven by the Robin $p$-Laplacian plus an indefinite potential. In the reaction we have the competing effects of a strictly $(p-1)$-sublinear parametric term and of a $(p-1)$-linear and nonuniformly nonresonant term. We study the set of positive solutions as the parameter $\lambda>0$ varies. We prove a bifurcation-type result for large values of the positive parameter $\lambda$. Also, we show that for all admissible $\lambda>0$, the problem has a smallest positive solution $\overline{u}_\lambda$ and we study the monotonicity and continuity properties of the map $\lambda\mapsto\overline{u}_\lambda$.

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Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. 2020-10-08. Positive solutions for the Robin $p$-Laplacian plus an indefinite potential. https://arxiv.org/abs/2010.03846

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