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arXiv · 2009.05960

Anisotropic equations with indefinite potential and competing nonlinearities

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

We consider a nonlinear Dirichlet problem driven by a variable exponent $p$-Laplacian plus an indefinite potential term. The reaction has the competing effects of a parametric concave (sublinear) term and of a convex (superlinear) perturbation (an anisotropic concave-convex problem). We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the positive parameter $\lambda$ varies. Also, we prove the existence of minimal positive solutions.

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Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. 2020-09-13. Anisotropic equations with indefinite potential and competing nonlinearities. https://doi.org/10.1016/j.na.2020.111861

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