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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 712306, 21 pages
Research Article

Well-Posedness for a Class of Strongly Mixed Variational-Hemivariational Inequalities with Perturbations

1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Scientific Computing Key Laboratory, Shanghai Universities, Shanghai 200234, China
3Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan
4Center for General Education, Kaohsiung Medical University, Kaohsiung 80708, Taiwan

Received 1 August 2011; Accepted 19 November 2011

Academic Editor: Ya Ping Fang

Copyright © 2012 Lu-Chuan Ceng et al. 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.


The concept of well-posedness for a minimization problem is extended to develop the concept of well-posedness for a class of strongly mixed variational-hemivariational inequalities with perturbations which includes as a special case the class of variational-hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed strongly mixed variational-hemivariational inequality and give some conditions under which the strongly mixed variational-hemivariational inequality is strongly well-posed in the generalized sense. On the other hand, it is also proven that under some mild conditions there holds the equivalence between the well posedness for a strongly mixed variational-hemivariational inequality and the well-posedness for the corresponding inclusion problem.