Existence of solution to a new class of coupled variational-hemivariational inequalities

TL;DR

This paper introduces a new class of coupled variational-hemivariational inequalities on Banach spaces, establishing the existence and compactness of solutions using advanced fixed point and nonsmooth analysis techniques.

Contribution

It develops a novel method combining multivalued fixed point principles with generalized monotonicity to analyze complex nonlinear coupled inequalities, extending previous results.

Findings

Proved the nonemptiness of the solution set.

Established the compactness of the solution set.

Generalized earlier theorems to a broader class of systems.

Abstract

The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We establish the nonemptiness and compactness of the solution set to the system. We apply a new method of proof based on a multivalued version of the Tychonoff fixed point principle in a Banach space combined with the generalized monotonicity arguments, and elements of the nonsmooth analysis. Our results improve and generalize some earlier theorems obtained for a very particular form of the system.