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Qualitative Analysis of Solutions for a Class of Anisotropic Elliptic Equations with Variable Exponent

Part of: Elliptic equations and systems Linear function spaces and their duals

Published online by Cambridge University Press:  15 December 2015

G. A. Afrouzi ,
M. Mirzapour  and
Vicenţiu D. Rădulescu
G. A. Afrouzi
Affiliation:
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran (afrouzi@umz.ac.ir; mirzapour@stu.umz.ac.ir)
M. Mirzapour
Affiliation:
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran (afrouzi@umz.ac.ir; mirzapour@stu.umz.ac.ir)
Vicenţiu D. Rădulescu*
Affiliation:
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia (vicentiu.radulescu@math.cnrs.fr) and Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy, PO Box 1-764, 014700 Bucharest, Romania
*
*Corresponding author.
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Abstract

We are concerned with the degenerate anisotropic problem

We first establish the existence of an unbounded sequence of weak solutions. We also obtain the existence of a non-trivial weak solution if the nonlinear term f has a special form. The proofs rely on the fountain theorem and Ekeland's variational principle.

Keywords

degenerate anisotropic Sobolev spacesvariable exponentDirichlet boundary value conditionfountain theoremEkeland variational principle

MSC classification

Secondary: 35J62: Quasilinear elliptic equations 35J70: Degenerate elliptic equations 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 3 , August 2016 , pp. 541 - 557
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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