An existence theorem for generalized variational inequalities with discontinuous and pseudomonotone operators |
| |
Authors: | BT Kien |
| |
Affiliation: | a Department of Information and Technology, Hanoi National University of Civil Engineering, 55 Giai Phong, Hanoi, Viet Namb Department of Applied Mathematics, Pukyong National University, Busan, 608-737, Republic of Korea |
| |
Abstract: | This paper gives a solution existence theorem for a generalized variational inequality problem with an operator which is defined on an infinite dimensional space, which is C-pseudomonotone in the sense of Inoan and Kolumbán D. Inoan, J. Kolumbán, On pseudomonotone set-valued mappings, Nonlinear Analysis 68 (2008) 47-53], but which may not be upper semicontinuous on finite dimensional subspaces. The proof of the theorem provides a new technique which reduces infinite variational inequality problems to finite ones. Two examples are given and analyzed to illustrate the theorem. Moreover, an example is presented to show that the C-pseudomonotonicity of the operator cannot be omitted in the theorem. |
| |
Keywords: | B-pseudomonotone operator K-pseudomonotone operator C-pseudomonotone operator Generalized variational inequality Solution existence |
本文献已被 ScienceDirect 等数据库收录! |
|