IJPAM: Volume 86, No. 1 (2013)
AN ELLIPTIC EQUATION WITH NONSTANDARD GROWTH
1Faculty of Economics and Administrative Sciences
2Faculty of Education
3Department of Mathematics
Abstract. This paper deals with the existence of solutions for some elliptic equations with nonstandard growth under zero Dirichlet boundary condition. Using a direct variational method and the theory of the variable exponent Sobolev spaces, we set some conditions that ensures the existence of nontrivial weak solutions.
Received: April 9, 2013
AMS Subject Classification: 35D05, 35J60, 35J70, 58E05
Key Words and Phrases: p(x)-Laplace operator, variable exponent Sobolev spaces, variational method, mountain pass theorem, Ekeland variational principle
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DOI: 10.12732/ijpam.v86i1.10 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395