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arXiv · 1704.02726

Robin problems with indefinite linear part and competition phenomena

N. S. Papageorgiou·V. D. Rădulescu·D. D. Repovš
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Abstract

We consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite potential. The reaction term involves competing nonlinearities. More precisely, it is the sum of a parametric sublinear (concave) term and a superlinear (convex) term. The superlinearity is not expressed via the Ambrosetti-Rabinowitz condition. Instead, a more general hypothesis is used. We prove a bifurcation-type theorem describing the set of positive solutions as the parameter $\lambda > 0$ varies. We also show the existence of a minimal positive solution $\tilde{u}_\lambda$ and determine the monotonicity and continuity properties of the map $\lambda \mapsto \tilde{u}_\lambda$.

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N. S. Papageorgiou, V. D. Rădulescu, D. D. Repovš. 2017-04-10. Robin problems with indefinite linear part and competition phenomena. https://doi.org/10.3934/cpaa.2017063

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