In this paper, we derive a general theorem concerning the quasi-variational inequality problem: find x̅ ∈ C and y̅ ∈ T(x̅) such that x̅ ∈ S(x̅) and ⟨y̅,z-x̅⟩ ≥ 0, ∀ z ∈ S(x̅), where C,D are two closed convex subsets of a normed linear space X with dual X*, and and are multifunctions. In fact, we extend the above to an existence result proposed by Ricceri [12] for the case where the multifunction T is required only to satisfy some general assumption without any continuity. Under a kind of Karmardian’s condition, we give a partial affirmative answer to an unbounded quasi-variational inequality problem.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1083,
author = {Liang-Ju Chu and Ching-Yang Lin},
title = {On discontinuous quasi-variational inequalities},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {27},
year = {2007},
pages = {199-212},
zbl = {1185.47072},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1083}
}
Liang-Ju Chu; Ching-Yang Lin. On discontinuous quasi-variational inequalities. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 27 (2007) pp. 199-212. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1083/
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