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In this paper, we study the existence of a weak solution for a class of Neumann boundary value problems for equations involving thep⁢(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.

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