Anisotropic equations with indefinite potential and competing nonlinearities. (December 2020)

• Record Type: Journal Article
• Authors: Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Repovš, Dušan D.
• Is Part Of: Nonlinear analysis. Volume 201(2020)
• Publication Date: 2020-12
• Subjects: 35J10 -- 35J70; Variable exponent spaces -- Regularity theory -- Maximum principle -- Concave and convex nonlinearities -- Positive solutions -- Comparison principles; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111861
• Languages: English
• ISSNs: 0362-546X

Abstract

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 a convex (superlinear) perturbation (the anisotropic concave–convex problem). We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the positive parameter λ varies. Also, we prove the existence of minimal positive solutions.