Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 201, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2020.111861
Keywords
Variable exponent spaces; Regularity theory; Maximum principle; Concave and convex nonlinearities; Positive solutions; Comparison principles
Categories
Funding
- Slovenian Research Agency [P1-0292, J1-8131, N1-0064, N1-0083, N1-0114]
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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. (C) 2020 Elsevier Ltd. All rights reserved.
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