Weak solution of a Neumann boundary value problem with 𝑝(𝑥)-Laplacian-like operator

Abstract In this paper, we study the existence of a weak solution for a class of Neumann boundary value problems for equations involving the p ⁢ ( x ) p(x) -Laplacian-like operator. Using a topological degree theory for a class of demicontinuous operators of generalized ( S + ) (S_{+}) -type and the theory of the variable exponent Sobolev spaces, we establish the existence of a weak solution of this problem. Our results extend and generalize several corresponding results from the existing literature.