Existence results for a class of hemivariational inequality problems on Hadamard manifolds |
| |
| Authors: | Guo-ji Tang Li-wen Zhou |
| |
| Institution: | 1. Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, Guangxi University for Nationalities, Nanning, P.R. China.;2. School of Science, Guangxi University for Nationalities, Nanning, P.R. China.;3. School of Sciences, Southwest Petroleum University, Chengdu, P.R. China. |
| |
| Abstract: | In this paper, a class of hemivariational inequality problems are introduced and studied on Hadamard manifolds. Using the properties of Clarke’s generalized directional derivative and Fan-KKM lemma, an existence theorem of solution in connection with the hemivariational inequality problem is obtained when the constraint set is bounded. By employing some coercivity conditions and the properties of Clarke’s generalized directional derivative, an existence result and the boundedness of the set of solutions for the underlying problem are investigated when the constraint set is unbounded. Moreover, a sufficient and necessary condition for ensuring the nonemptiness of the set of solutions concerned with the hemivariational inequality problem is also given. |
| |
| Keywords: | Hemivariational inequality generalized directional derivative locally Lipschitz function Fan-KKM lemma Hadamard manifold |
|
|
