Abstract and Applied Analysis
Volume 2003 (2003), Issue 10, Pages 601-619

Existence results for general inequality problems with constraints

George Dincă,1 Petru Jebelean,2 and Dumitru Motreanu3

1Department of Mathematics, University of Bucharest, St. Academiei, no.14, Bucharest 70109, Romania
2Department of Mathematics, West University of Timişoara, Bv. V. Pârvan, no. 4, Timişoara 1900, Romania
3Département de Mathématiques, Université de Perpignan, 52, avenue de Villeneuve, Perpignan Cedex 66860, France

Received 25 February 2002

Copyright © 2003 George Dincă 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.


This paper is concerned with existence results for inequality problems of type F0(u;v)+Ψ(u;v)0, for all vX, where X is a Banach space, F:X is locally Lipschitz, and Ψ:X(+] is proper, convex, and lower semicontinuous. Here F0 stands for the generalized directional derivative of F and Ψ denotes the directional derivative of Ψ. The applications we consider focus on the variational-hemivariational inequalities involving the p-Laplacian operator.