Existence and multiplicity of solutions for a general p(x)-Laplacian Neumann problem

In this paper, we verify that a general p(x)$p\left(x\right)$-Laplacian Neumann problem has at least three weak solutions, which generalizes the corresponding result of the reference Mihai Mihilescu, Existence and multiplicity of solutions for a Neumann problem involving the p(x)$p\left(x\right)$-Laplace operator, Nonlinear Anal. 67 (2007) 1419–1425].