Existence results for a class of hemivariational inequalities involving the stable $(g,f,\alpha)$-quasimonotonicity

Abstract

In this paper, by introducing a new concept of the stable $(g,f,\alpha)$-quasimonotonicity and applying the properties of Clarke's generalized gradient and KKM technique, we show the existence results of solutions for hemivariational inequalities when the constraint set is compact, bounded and unbounded, respectively, which extends and improves several well-known results in many respects. In the last section, we also give an example to present the our main result.