Weak Solutions for a Quasilinear Elliptic and Parabolic Problems Involving the (p(x), q(x))-Laplacian Operator

Abstract

A. In the present paper, in view of the topological degree methods and the theory of the variable exponent Sobolev spaces, we discuss some quasilinear problems for elliptic and parabolic equations involving the (p(x), q(x))-Laplacian operator.Under certain assumptions, we establish the existence of at least one weak solution to these problems.Our results extends some recent work in the literature.