Geodesic
Variational inequalities in noncompact nonconvex regions
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 23 (2003) no. 1, pp. 5-19.

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In this paper, a general existence theorem on the generalized variational inequality problem GVI(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 V₀-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 GVI(T,C,ϕ), which generalizes a result of Fang and Peterson.
Keywords: Nikaidô's coincidence theorem, variational inequality, nearly convex, V₀-Karamardian condition, Saigal condition, acyclic multifunction, algebraic interior, bounding points 
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Lin, Ching-Yan; Chu, Liang-Ju. Variational inequalities in noncompact nonconvex regions. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 23 (2003) no. 1, pp. 5-19. http://geodesic.mathdoc.fr/item/DMDICO_2003_23_1_a0/

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