Infinitely many solutions for a class of hemivariational inequalities involving p(x)-Laplacian

In this paper hemivariational inequality with nonhomogeneous Neumann boundary condition is investigated. The existence of infinitely many small solutions involving a class of p(x) - Laplacian equation in a smooth bounded domain is established. Our main tool is based on a version of the symmetric mountain pass lemma due to Kajikiya and the principle of symmetric criticality for a locally Lipschitz functional.

Multiple solutions for an inclusion quasilinear problem with nonhomogeneous boundary condition through Orlicz–Sobolev spaces

In this work, we study multiplicity of nontrivial solution for the following class of differential inclusion problems with nonhomogeneous Neumann condition through Orlicz–Sobolev spaces, [Formula: see text] where [Formula: see text] is a domain, [Formula: see text] and [Formula: see text] is the generalized gradient of [Formula: see text]. The main tools used are Variational Methods for Locally Lipschitz Functional and Critical Point Theory.

Existence, comparison, and compactness results for quasilinear variational-hemivariational inequalities

We consider quasilinear elliptic variational-hemivariational inequalities involving the indicator function of some closed convex set and a locally Lipschitz functional. We provide a generalization of the fundamental notion of sub- and supersolutions, on the basis of which we then develop the sub-supersolution method for variational-hemivariational inequalities, including existence, comparison, compactness, and extremality results.