Existence of weak solutions for elliptic Dirichlet problems with variable exponent

Abstract

. This paper presents several sufficient conditions for the existence of weak solutions to general nonlinear elliptic problems of the type where Ω is a bounded domain of R n , n > 2. In particular, we do not require strict monotonicity of the principal part a ( x, z, · ), while the approach is based on the variational method and results of the variable exponent function spaces.