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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