A class of quasi-variational inequalities (QVI) of elliptic type is studied in reflexive Banach spaces. The concept of QVI was earlier introduced by A. Bensoussan and J.-L. Lions [2] and its general theory has been developed by many mathematicians, for instance, see [6, 7, 9, 13] and a monograph [1]. In this paper we give a generalization of the existence theorem established in [14]. In our treatment we employ the compactness method along with a concept of convergence of nonlinear multivalued operators of monotone type (cf. [11]). We shall prove an abstract existence result for our class of QVI's, and moreover, give some applications to QVI's for elliptic partial differential operators.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-15,
author = {Yusuke Murase},
title = {Abstract quasi-variational inequalities of elliptic type and applications},
journal = {Banach Center Publications},
volume = {86},
year = {2009},
pages = {235-246},
zbl = {1183.47061},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-15}
}
Yusuke Murase. Abstract quasi-variational inequalities of elliptic type and applications. Banach Center Publications, Tome 86 (2009) pp. 235-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-15/