Publications of Varga, Csaba

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 [21]. 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.

Multiplicity results for some elliptic problems with nonlinear boundary conditions involving variable exponents

In this paper we analyze an elliptic partial differential equation involving variable exponent growth conditions coupled with a nonlinear boundary condition. We show the existence of infinitely many bounded weak solutions provided there is a suitable oscillatory behavior of the nonlinearity either at infinity or at zero. Our proofs rely on a method due to Saint Raymond.

Multiplicity results for double eigenvalue problems involving the p-Laplacian

The existence of multiple nontrivial solutions for two types of double eigenvalue problems involving the p-Laplacian is derived. To prove the existence of at least two nontrivial solutions we use a Ricceri-type three critical point result for non-smooth functions of S. Marano and D. Motreanu \cite{MarMot}. The existence of at least three nontrivial solutions is shown by combining a result of B. Ricceri \cite{Ricceri} and a Pucci-Serrin mountain pass type theorem of S. Marano and D. Motreanu \cite{MarMot}.