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

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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
Keywords:variable exponent spaces, regularity theory, maximum principle, concave and convex nonlinearities, positive solutions, comparison principles
Work type:Article (dk_c)
Tipology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
Year:2020
Number of pages:art. 111861 (24 str.)
Numbering:Vol. 201
UDC:517.956
ISSN on article:0362-546X
DOI:10.1016/j.na.2020.111861 This link opens in a new window
COBISS.SI-ID:18953305 This link opens in a new window
Views:198
Downloads:151
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Record is a part of a journal

Title:Nonlinear Analysis
Shortened title:Nonlinear anal.
Publisher:Pergamon Press
ISSN:0362-546X
COBISS.SI-ID:26027520 This link opens in a new window

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