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On the solution existence of generalized quasivariational inequalities with discontinuous multifunctions

Bui Trong Kien Ngai-Ching Wong Jen-Chih Yao

Spectral Theory and Operator Algebra mathscidoc:1910.43651

Journal of Optimization Theory and Applications, 135, (3), 515-530, 2007.12
We study the following generalized quasivariational inequality problem: given a closed convex set <i>X</i> in a normed space <i>E</i> with the dual <i>E</i> <sup>*</sup>, a multifunction \Phi :Xightarrow 2^{E^{*}} and a multifunction :<i>X</i>2<sup> <i>X</i> </sup>, find a point \Phi :Xightarrow 2^{E^{*}} such that \Phi :Xightarrow 2^{E^{*}} , \Phi :Xightarrow 2^{E^{*}} . We prove some existence theorems in which may be discontinuous, <i>X</i> may be unbounded, and is not assumed to be Hausdorff lower semicontinuous.
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@inproceedings{bui2007on,
  title={On the solution existence of generalized quasivariational inequalities with discontinuous multifunctions},
  author={Bui Trong Kien, Ngai-Ching Wong, and Jen-Chih Yao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020205521620019180},
  booktitle={Journal of Optimization Theory and Applications},
  volume={135},
  number={3},
  pages={515-530},
  year={2007},
}
Bui Trong Kien, Ngai-Ching Wong, and Jen-Chih Yao. On the solution existence of generalized quasivariational inequalities with discontinuous multifunctions. 2007. Vol. 135. In Journal of Optimization Theory and Applications. pp.515-530. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020205521620019180.
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