On the browder-hartman-stampacchia variational inequality

  • Chang, S.S. (Department of Mathematics Sichuan University) ;
  • Ha, K.S. (Department of Mathematics Pusan National University) ;
  • Cho, Y.J. (Department of Mathematics Gyeongsang National University) ;
  • Zhang, C.J. (Department of Mathematics Huaibei Coal Teachers College)
  • Published : 1995.08.01

Abstract

The Hartman-Stampacchia variational inequality was first suggested and studied by Hartman and Stampacchia [8] in finite dimensional spaces during the time establishing the base of variational inequality theory in 1960s [4]. Then it was generalized by Lions et al. [6], [9], [10], Browder [3] and others to the case of infinite dimensional inequality [3], [9], [10], and the results concerning this variational inequality have been applied to many important problems, i.e., mechanics, control theory, game theory, differential equations, optimizations, mathematical economics [1], [2], [6], [9], [10]. Recently, the Browder-Hartman-Stampaccnia variational inequality was extended to the case of set-valued monotone mappings in reflexive Banach sapces by Shih-Tan [11] and Chang [5], and under different conditions, they proved some existence theorems of solutions of this variational inequality.