On the Robin problem with indefinite weight in Sobolev spaces with variable exponents
type: Item
instance of: scholarly article
title: On the Robin problem with indefinite weight in Sobolev spaces with variable exponents
zbMATH Open document ID: 1392.35126
DOI: 10.4171/ZAA/1600
author: Khaled Kefi
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2018-03-23T00:00:00Z
review text: Summary: The present paper is concerned with a Robin problem involving an indefinite weight in Sobolev spaces with variable exponents \[ \begin{cases}\quad\quad-\mathrm{div}(|\nabla u|^{p(x)-2}\nabla u)=\lambda V(x)|u|^{q(x)-2}u,&x\in\Omega\\|\nabla u|^{p(x)-2}\frac{\partial u}{\partial n}+a(x)|u|^{p(x)-2}u=0.& x\in\Omega\end{cases} \] By means of the variational approach and Ekeland's principle, we establish that the above problem admits a non-trivial weak solution under appropriate conditions.
Mathematics Subject Classification ID: 35J58
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J35
zbMATH DE Number: 6852539
zbMATH Keywords: \(p(x)\)-Laplacian
zbMATH Keywords: Robin problem
zbMATH Keywords: Ekeland's variational principle
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6852539