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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1042,
author = {Ching-Yan Lin and Liang-Ju Chu},
title = {Variational inequalities in noncompact nonconvex regions},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {23},
year = {2003},
pages = {5-19},
zbl = {1054.47054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1042}
}
Ching-Yan Lin; Liang-Ju Chu. Variational inequalities in noncompact nonconvex regions. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 23 (2003) pp. 5-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1042/
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