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Abstract and Applied Analysis
Volume 2010, Article ID 472760, 9 pages
Research Article

Some Existence Theorems for Nonconvex Variational Inequalities Problems

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 9 November 2010; Accepted 18 December 2010

Academic Editor: Roman Dwilewicz

Copyright © 2010 Narin Petrot. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By using nonsmooth analysis knowledge, we provide the conditions for existence solutions of the variational inequalities problems in nonconvex setting. We also show that the strongly monotonic assumption of the mapping may not need for the existence of solutions. Consequently, the results presented in this paper can be viewed as an improvement and refinement of some known results from the literature.