EXISTENCE AND UNIQUENESS RESULTS FOR PARAMETRIC MIXED VARIATIONAL-HEMIVARIATIONAL PROBLEMS

Tóm tắt

In this paper, we introduce a general class of parametric mixed variational-hemivariational problems involving the Clarke's generalized derivatives and equilibrium functions (for brevity, PMVHP). Then, based on the technique involving the Tarafdar’s fixed point theorem and some arguments in the nonsmooth analysis, the existence of solutions for the problem PMVHP is studied. Furthermore, we establish the uniqueness of the solution to the problem PMVHP under some strong monotonicity assumptions. Our main results in this paper extend the corresponding results in Matei (2019, 2022).