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

Published online by Cambridge University Press:  15 December 2015

G. A. Afrouzi
Affiliation:
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran ([email protected]; [email protected])
M. Mirzapour
Affiliation:
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran ([email protected]; [email protected])
Vicenţiu D. Rădulescu*
Affiliation:
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia ([email protected]) and Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy, PO Box 1-764, 014700 Bucharest, Romania
*
*Corresponding author.

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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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