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

Subject Areas : International Journal of Industrial Mathematics

‎Ayed E. ‎‎Hashoosh‎ ¹ , M. Alimohammady‎ ²

1 - Department of Mathematics, University of Thi-Qar, Nasiriyah, Iraq.
2 - Department of Mathematics, University of Mazandran, Babolsar, Iran.

Received: 2017-09-05 Accepted : 2017-09-05 Published : 2017-07-01

Keywords: Set-valued operator, Clarke's generalized gradian, Generalized monotonicity, Variational-hemivariational in, Differential ‎inclusion.‎,

Abstract :

‎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.