Combined effects of concave–convex nonlinearities and indefinite potential in some elliptic problems

Abstract

We consider a nonlinear Dirichlet problem driven by the p-Laplacian and a reaction which exhibits the combined effects of concave (that is, sublinear) terms and of convex (that is, superlinear) terms. The concave term is indefinite and the convex term need not satisfy the usual in such cases Ambrosetti–Rabinowitz condition. We prove a bifurcation-type result describing the set of positive solutions as the positive parameter λ varies.

Keywords

indefinite concave term superlinear perturbation nonlinear regularity positive solutions

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