Anisotropic equations with indefinite potential and competing nonlinearities

Nikolaos Socrates Papageorgiou (Author), Vicenţiu Rǎdulescu (Author), Dušan Repovš (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.

Keywords

variable exponent spaces;regularity theory;maximum principle;concave and convex nonlinearities;positive solutions;comparison principles;

Data

Language:	English
Year of publishing:	2020
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	517.956
COBISS:	18953305
ISSN:	0362-546X
Views:	360
Downloads:	202
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	art. 111861 (24 str.)
Issue:	ǂVol. ǂ201
Chronology:	Dec. 2020
DOI:	10.1016/j.na.2020.111861
ID:	12036911