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 variationalhemivariational 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. Finally, we enhance the main results by the application of some differential inclusions.