Existence and uniqueness results for a class of quasi-hemivariational inequalities

AbstractIn this paper we are concerned with the study of a nonstandard quasi-hemivariational inequality. Using a fixed point theorem for set-valued mappings the existence of at least one solution in bounded closed and convex subsets is established. We also provide sufficient conditions for which our inequality possesses solutions in the case of unbounded sets. Finally, the uniqueness and the stability of the solution are analyzed in a particular case

Systems of nonlinear hemivariational inequalities and applications

In this paper we prove several existence results for a general class of systems of nonlinear hemivariational inequalities by using a fixed point theorem of Lin (Bull. Austral. Math. Soc. {\bf 34}, (1986), 107-117). Our analysis includes both the cases of bounded and unbounded closed convex subsets in real reflexive Banach spaces. In the last section we apply the abstract results obtained to extend some results concerning nonlinear hemivariational inequalities, to establish existence results of Nash generalized derivative points and to prove the existence of at least one weak solution for an electroelastic contact problem