On the well-posedness of differential quasi-variational-hemivariational inequalities

Abstract

The goal of this paper is to discuss the well-posedness and the generalized well-posedness of a new kind of differential quasi-variational-hemivariational inequality (DQHVI) in Hilbert spaces. Employing these concepts, we explore the essential relation between metric characterizations and the well-posedness of DQHVI. Moreover, the compactness of the set of solutions for DQHVI is delivered, when problem DQHVI is well-posed in the generalized sense.

Keywords

• differential quasi-variational-hemivariational inequality
• well-posedness
• approximating sequence
• α-monotonicity
• 47h04
• 49j53
• 90c31