Evolutionary variational–hemivariational inequalities: Existence and comparison results

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,...

Existence Results for General Mixed Quasivariational Inequalities

Existence Results for Vector Variational- like Inequalities

In this paper, we consider and study a class of vector variational-like inequalities in Banach space without any generalized monotonicity by exploiting vector version of minimax inequality and obtain the existence results of solutions to the class of vector variational-like inequalities. The results presented here are different from [1, 5, 11], and extend and generalize the corresponding result...