Existence of three solutions for variable exponent elliptic systems
type: Item
instance of: scholarly article
title: Existence of three solutions for variable exponent elliptic systems
zbMATH Open document ID: 1332.35100
author: Mostafa Allaoui
published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche
publication date: 2015-12-07T00:00:00Z
review text: The author investigates the existence of solutions for the elliptic system \[ \Delta(|\Delta u|^{p(x)-2}\Delta u)=\lambda F_u(x,u,v)+\mu G_u(x,u,v), \] \[ \Delta(|\Delta v|^{q(x)-2}\Delta v)=\lambda F_v(x,u,v)+\mu G_v(x,u,v), \] in a smooth open and bounded subset of \({\mathbb R}^N\), \(N\geq 1\). The system is complemented with Navier boundary conditions. Under some additional conditions the author obtains the existence of at least three weak solutions. The approach relies on a three critical point theorem due to Ricceri.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35J35
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35B38
zbMATH DE Number: 6516559
zbMATH Keywords: Navier value problem
zbMATH Keywords: variable exponent Sobolev space
zbMATH Keywords: critical point theorem
MaRDI profile type: Publication
full work available at URL: s11565-015-0225-8
OpenAlex ID: W2093206682
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DOI: 10.1007/S11565-015-0225-8
description: scientific article; zbMATH DE number 6516559