Abstract
In this paper we are concerned with the study of a hemivariationalinequality with nonhomogeneous Neumann boundary condition. Weestablish the existence of at least three solutions of the problem by usingthe nonsmooth three critical points theorem and the principle of symmetriccriticality for Motreanu-Panagiotopoulos type functionals.
Highlights
∀u ∈ W01,p(x)(Ω), ∀u ∈ W01,p(x)(Ω), The p(x)−Laplace operator ∆p(x)u = div(|∇u|p(x)−2∇u) is a natural generalization of the p−Laplacian operator ∆pu = div(|∇u|p−2∇u), where p > 1 is a real constant
Differential equations and variational problems have been studied in many papers, we refer to some interesting works
For a thorough treatment of the hemivariational inequality problems we refer to the monographs Naniewicz and Panagiotopoulos, Motreanu and Panagiotopoulos, Motreanu and Rádulescu
Summary
(cf [24]) Let X be a Banach space, I : X →
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