Existence of weak solutions for p(x)-Laplacian-like problem with p(x)-Laplacian operator under Neumann boundary condition

Our purpose is to establish the existence of weak solutions to Neumann boundary value problem for equations involving the p ( x )-Laplacian-like operator and the p ( x )-Laplacian operator. The existence proof is based on the theory of the variable exponent Sobolev spaces and the topological degree theory. Our result extend and generalize several corresponding results from the existing literature.