Variational inequalities in noncompact nonconvex regions
Liang-Ju Chu, Ching-Yan Lin · Discussiones Mathematicae Differential Inclusions Control and Optimization · 2003
In this paper, a general existence theorem on the generalized variational inequality problem GV I(T, C, φ) is derived by using our new versions of Nikaidô's coincidence theorem, for the case where the region C is noncompact and nonconvex, but merely is a nearly convex set.Equipped with a kind of V 0 -Karamardian condition, this general existence theorem contains some existing ones as special cases.Based on a Saigal condition, we also modify the main theorem to obtain another existence theorem on GV I(T, C, φ), which generalizes a result of Fang and Peterson.