Evolutionary Quasi-Variational-Hemivariational Inequalities I: Existence and Optimal Control

Existence and Comparison Results for Variational-hemivariational Inequalities

We consider a prototype of 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 suband supersolutions on the basis of which we then develop the sub-supersolution method for variationalhemivariational inequalities. Furthermore, we give a...

Existence and Uniqueness Results for a Nonstandard Variational-Hemivariational Inequalities with Application

‎This paper aims at establishing the existence and uniqueness of solutions for a nonstandard variational-hemivariational inequality. The solutions of this inequality are discussed in a subset $K$ of a reflexive Banach space $X$. Firstly, we prove the existence of solutions in the case of bounded closed and convex subsets. Secondly, we also prove the case when $K$ is compact convex subsets. Fina...

Existence Results for Quasi Variational Inequalities

It is well known that the quasi variational inequalities are equivalent to the fixed point problems. We this equivalent alternative formulation to discuss the existence of a solution of quasi variational inequalities under some mild conditions. Since the quasi variational inequalities include variational inequalities, implicit complementarity problems and optimization problems as special cases,...

On Variational and Hemivariational Inequalities Author

Advances in Variational and Hemivariational Inequalities

We consider a nonlinear Dirichlet parametric problem with discontinuous right hand side in which we have a competing effect of sub and superlinear nonlinearities. A bifurcation type result is studied when the parameter tends to zero.