Weak solutions for double phase problem driven by the (p(x),q(x))-Laplacian operator under Dirichlet boundary conditions

Abstract

In the present paper, in view of the topological degree methods and the theory of the variable exponent Sobolev spaces, we discuss a Dirichlet boundary value problem for elliptic equations involving the $(p(x),q(x))$-Laplacian operator with a reaction term depending on the gradient and on two real parameters. Under certain assumptions, we establish the existence of at least one weak solution to this problem. Our results extends some recent work in the literature.