Systems of nonlinear hemivariational inequalities and applications

Nicuşor Costea, Csaba Varga

Abstract


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.

Keywords


Nonlinear hemivariational inequality; set-valued operator; nonsmooth functions; Clarke's generalized gradient; Nash generalized derivative point; piezoelectric body

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