Anisotropic Robin problems with logistic reaction
type: Item
instance of: scholarly article
title: Anisotropic Robin problems with logistic reaction
zbMATH Open document ID: 1466.35228
author: Nikolaos S. Papageorgiou
author: Vicenţiu D. Rădulescu
author: X. H. Tang
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2021-05-19T00:00:00Z
review text: The paper deals with existence results of positive solutions for elliptic equations driven by the \(p(x)\)-Laplacian (so-called anisotropic \(p\)-Laplacian) involving a nonnegative potential and a right-hand side depending on a parametric term with exponent \(q(x)\) and a perturbation \(f\). Here, the boundary condition is of Robin-type. The authors discuss in a very precise way the cases when the equation is superdiffusive, subdiffusive and equidiffusive. In the superdiffusive case the existence of a bifurcation point \(\lambda^*\) is shown so that for large parameters, the equation has at least two positive smooth solution, at least one positive smooth solution when the parameter is equal \(\lambda^*\) and no positive solution when the parameter is less than \(\lambda^*\). In the subdiffusive case the authors obtain uniqueness of the positive solutions and for the equidiffusive case uniqueness and nonexistence is shown. In this last case the results are only obtained in the isotropic case which is due to the fact, that is not known if the first eigenvalue of the anisotropic \(p\)-Laplacian with Neumann boundary condition is positive.
reviewed by: Patrick Winkert
Mathematics Subject Classification ID: 35J92
Mathematics Subject Classification ID: 35J66
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 7349705
zbMATH Keywords: anisotropic \(p\)-Laplacian
zbMATH Keywords: logistic reaction
zbMATH Keywords: positive solutions
zbMATH Keywords: multiplicity and uniqueness of positive solutions
zbMATH Keywords: regularity theory
zbMATH Keywords: maximum principle
MaRDI profile type: Publication
full work available at URL: s00033-021-01514-w
OpenAlex ID: W3177192859
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DOI: 10.1007/S00033-021-01514-W
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description: scientific article; zbMATH DE number 7349705