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

Article type: Research Article

Authors: Papageorgiou, Nikolaos S.^a | Rădulescu, Vicenţiu D.^{b; c; *}

Affiliations: [a] Department of Mathematics, National Technical University, Athens, Greece. E-mail: npapg@math.ntua.gr | [b] Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah, Saudi Arabia | [c] Institute of Mathematics “Simion Stoilow” of the Romanian Academy, Bucharest, Romania. E-mail: vicentiu.radulescu@math.cnrs.fr

Correspondence: [*] Corresponding author: Vicenţiu D. Rădulescu, Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania. E-mail: vicentiu.radulescu@math.cnrs.fr.

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, p-Laplacian, nonlinear regularity, positive solutions

DOI: 10.3233/ASY-151292

Journal: Asymptotic Analysis, vol. 93, no. 3, pp. 259-279, 2015