Nicuşor Costea

Hartman–Stampacchia results for stably pseudomonotone operators and non-linear hemivariational inequalities

We are concerned with two classes of non-standard hemivariational inequalities. In the first case we establish a Hartman–Stampacchia type existence result in the framework of stably pseudomonotone operators. Next, we prove an existence result for a class of non-linear perturbations of canonical hemivariational inequalities. Our analysis includes both the cases of compact sets and of closed convex sets in Banach spaces. Applications to non-coercive hemivariational and variational–hemivariational inequalities illustrate the abstract results of this article.

Inequality problems of quasi-hemivariational type involving set-valued operators and a nonlinear term

The aim of this paper is to establish the existence of at least one solution for a general inequality of quasi-hemivariational type, whose solution is sought in a subset K of a real Banach space E. First, we prove the existence of solutions in the case of compact convex subsets and the case of bounded closed and convex subsets. Finally, the case when K is the whole space is analyzed and necessary and sufficient conditions for the existence of solutions are stated. Our proofs rely essentially on the Schauder’s fixed point theorem and a version of the KKM principle due to Ky Fan (Math Ann 266:519–537, 1984).

On a class of variational-hemivariational inequalities involving set valued mappings

Abstract Using the KKM technique, we establish some existence results for variational-hemivariational inequalities involving monotone set valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive several sufficient conditions for the existence of solutions in the case of unbounded subsets.

Antiplane shear deformation of piezoelectric bodies in contact with a conductive support

We consider a mathematical model which describes the frictional contact between a piezoelectric body and an electrically conductive support. We model the material’s behavior with an electro-elastic constitutive law; the frictional contact is described with a boundary condition involving Clarke’s generalized gradient and the electrical condition on the contact surface is modelled using the subdifferential of a proper, convex and lower semicontinuous function. We derive a variational formulation of the model and then, using a fixed point theorem for set valued mappings, we prove the existence of at least one weak solution. Finally, the uniqueness of the solution is discussed; the investigation is based on arguments in the theory of variational-hemivariational inequalities.