Anisotropic equations with indefinite potential and competing nonlinearities
Papageorgiou, Nikolaos (Author), Rǎdulescu, Vicenţiu (Author), Repovš, Dušan (Author)

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 ▫$\lambda$▫ varies. Also, we prove the existence of minimal positive solutions.

Language: English variable exponent spaces, regularity theory, maximum principle, concave and convex nonlinearities, positive solutions, comparison principles Article (dk_c) 1.01 - Original Scientific Article PEF - Faculty of Education 2020 art. 111861 (24 str.) Vol. 201 517.956 0362-546X 10.1016/j.na.2020.111861 18953305 198 151 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

## Record is a part of a journal

Title: Nonlinear Analysis Nonlinear anal. Pergamon Press 0362-546X 26027520