Solutions with sign information for nonlinear nonhomogeneous elliptic equations
type: Item
instance of: scholarly article
title: Solutions with sign information for nonlinear nonhomogeneous elliptic equations
zbMATH Open document ID: 1375.35126
DOI: 10.12775/TMNA.2015.027
author: Nikolaos S. Papageorgiou
author: Vicenţiu D. Rădulescu
published in: Topological Methods in Nonlinear Analysis
publication date: 2017-05-08T00:00:00Z
review text: The paper deals with the existence of multiple nontrivial solutions to the Dirichlet problem \[ \begin{cases} -\text{div\,}a(Du(z))=f(x,u(z)) & \text{in}\;\Omega,\\ u=0 & \text{on}\;\partial\Omega, \end{cases} \] where \(\Omega\subset \mathbb{R}^N\) is a bounded and \(C^2\)-smooth domain, the map \(a:\;\mathbb{R}^N\to \mathbb{R}^N\) is strictly monotone and \(f\) is a Carathéodory function. The authors show the existence of at least three nontrivial solutions, all with sign information, by means of variational methods combined with truncation and comparison techniques. In the particular case of \((p,2)\)-equations, tools from Morse theory are employed to show the existence of four nontrivial solutions. Finally, for a special class of parametric equations, multiplicity theorems are obtained that generalize earlier results on the subject.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 6712491
zbMATH Keywords: nonlinear elliptic equations
zbMATH Keywords: Dirichlet problem
MaRDI profile type: Publication
full work available at URL: tmna.2015.027
OpenAlex ID: W2293257762
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description: scientific article; zbMATH DE number 6712491