The Solvability of Generalized Systems of Time-Dependent Hemivariational Inequalities Enjoying Symmetric Structure in Reflexive Banach Spaces

In real reflexive Banach spaces, let the GSTDHVI, SHVI, DVIP, VIT, and KKM represent a generalized system of time-dependent hemivariational inequalities, a system of hemivariational inequalities, a derived vector inclusion problem, Volterra integral term, and Knaster-Kuratowski-Mazurkiewicz, respectively, where the GSTDHVI consists of two parts which are of symmetric structure mutually. By virtue of the surjectivity theorem for pseudo-monotonicity mappings and the Banach contraction mapping principle, instead of the KKM theorems exploited by other authors in recent literature for a SHVI, we consider and study a GSTDHVI with VITs. Under quite mild assumptions, it is shown that there exists only a solution to the investigated problem via demonstrating that a DVIP with VIT is solvable.

Automated summary

In this study, a generalized system of time-dependent hemivariational inequalities with Volterra integral terms was considered and it was shown that a derived vector inclusion problem with VIT is solvable, leading to the conclusion that there exists only one solution to the investigated problem.