Abstract and Applied Analysis 
Volume 2003 (2003), Issue 10, Pages 601-619
doi:10.1155/S1085337503210058

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

Abstract

This paper is concerned with existence results for inequality problems of type F0(u;v)+Ψ′(u;v)≥0, for all v∈X, where X is a Banach space, F:X→ℝ 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.