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Volume 6, Issue 5, 1 October 2022, Pages 499-516
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 proof based on a multivalued version of the Tychonoff fixed point principle in a Banach space combined with the generalized monotonicity arguments, and the elements of the nonsmooth analysis. Our results improve and generalize some earlier theorems obtained for a particular form of the system.
How to Cite this Article:
Yunru Bai, Stanislaw Migórski, Van Thien Nguyen, Jianwen Peng, Existence of solutions to a new class of coupled variational-hemivariational inequalities, J. Nonlinear Var. Anal. 6 (2022), 499-516.