tailieunhanh - Báo cáo hóa học: " Research Article The Nonzero Solutions and Multiple Solutions for a Class of Bilinear Variational Inequalities Jianhua Huang"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article The Nonzero Solutions and Multiple Solutions for a Class of Bilinear Variational Inequalities Jianhua Huang | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 94808 9 pages doi 2007 94808 Research Article The Nonzero Solutions and Multiple Solutions for a Class of Bilinear Variational Inequalities Jianhua Huang Received 24 May 2007 Accepted 29 June 2007 Recommended by Donal O Regan Some existence theorems of nonzero solutions and multiple solutions for a class of bilinear variational inequalities are studied in reflexive Banach spaces by fixed point index approach. The results presented in this paper improve and extend some known results in the literature. Copyright 2007 Jianhua Huang. 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. 1. Introduction and preliminaries The fundamental theory of the variational inequalities since it was founded in the 1960 s has made powerful progress and has played an important role in nonlinear analysis. It has been applied intensively to mechanics partial differential equation problems with boundary conditions control theory game theory optimization methods nonlinear programming and so forth see 1 . In 1987 Noor 2 studied Signorini problem in the framework of the following variational inequality a u u - v b u u - b u v g u u - v Vv e K and proved the existence of solutions of Signorini problem in Hilbert spaces. In 1991 Zhang and Xiang 3 studied the existence of solutions of bilinear variational inequality in reflexive Banach space X. As an application they discussed the existence of solutions for Signorini problem. Throughout this paper we assume that X is a reflexive space X is the dual space of X is the pair between X and X K is a nonempty closed convex subset of X with 2 Journal of Inequalities and Applications 0 e K and for r 0 Kr x e K xh r . Suppose that a X XX R -TO ro is a coercive and bilinear continuous .