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

Document Type : Research Paper


1 Department of Mathematics, University of Thi-Qar, Nasiriyah, Iraq.

2 Department of Mathematics, University of Mazandran, Babolsar, ‎Iran.


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