Anisotropic equations with indefinite potential and competing nonlinearities

Papageorgiou, Nikolaos S. (author), Rǎdulescu, Vicenţiu (author), Repovš, Dušan (author)

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
• Keywords: variable exponent spaces, regularity theory, maximum principle, concave and convex nonlinearities, positive solutions, comparison principles
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2020
• Number of pages: art. 111861 (24 str.)
• Numbering: Vol. 201
• PID: 20.500.12556/RUL-119968
• UDC: 517.956
• ISSN on article: 0362-546X
• DOI: 10.1016/j.na.2020.111861
• COBISS.SI-ID: 18953305
• Publication date in RUL: 14.09.2020

Record is a part of a journal

• Title: Nonlinear Analysis
• Shortened title: Nonlinear anal.
• Publisher: Pergamon Press
• ISSN: 0362-546X
• COBISS.SI-ID: 26027520