- Volume 32 Issue 3
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
The Hartman-Stampacchia variational inequality was first suggested and studied by Hartman and Stampacchia  in finite dimensional spaces during the time establishing the base of variational inequality theory in 1960s . Then it was generalized by Lions et al. , , , Browder  and others to the case of infinite dimensional inequality , , , 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 , , , , . Recently, the Browder-Hartman-Stampaccnia variational inequality was extended to the case of set-valued monotone mappings in reflexive Banach sapces by Shih-Tan  and Chang , and under different conditions, they proved some existence theorems of solutions of this variational inequality.