AN INVERSE PROBLEM FOR A CLASS OF QUASI-HEMIVARIATIONAL INEQUALITIES ON CONSTANT CURVATURE HADAMARD MANIFOLDS

In this paper, we investigate a class of quasi-hemivariational inequalities involving the generalized subdifferentials in the sense of Clarke and the set-valued constraint in the setting of constant curvature Hadamard manifolds. Using the Kakutani-Fan-Glicksberg type fixed point theorem for multi-valued maps on Hadamard manifolds, we prove the nonemptiness and compactness of the solution set of such problems under suitable assumptions. The other goal of the paper is to consider a nonlinear inverse problem, which is described as a regularized optimal control problem for the quasi-hemivariational inequality on Hadamard manifolds and provide the existence result.