caa a22 4500 46316962X CHVBK 20180406164809.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s10957-007-9239-4 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9239-4 On the Solution Existence of Generalized Quasivariational Inequalities with Discontinuous Multifunctions [Elektronische Daten] [B. Kien, N. Wong, J. Yao] We study the following generalized quasivariational inequality problem: given a closed convex set X in a normed space E with the dual E *, a multifunction $\Phi :X\rightarrow 2^{E^{*}}$ and a multifunction Γ:X→2 X , find a point $(\hat{x},\hat{z})\in X\times E^{*}$ such that $\hat{x}\in \Gamma(\hat{x}),\hat{z}\in \Phi (\hat{x}),\langle \hat{z},\hat{x}-y\rangle \leq 0$ , $\forall y\in \Gamma(\hat{x})$ . We prove some existence theorems in which Φ may be discontinuous, X may be unbounded, and Γ is not assumed to be Hausdorff lower semicontinuous. Springer Science+Business Media, LLC, 2007 Generalized quasivariational inequalities nationallicence Lower semicontinuity nationallicence Hausdorff upper semicontinuity nationallicence Hausdorff lower semicontinuity nationallicence Multifunctions nationallicence Closed graphs nationallicence Open graphs nationallicence Kien B. Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC aut Wong N. Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC aut Yao J. Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC aut Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 135/3(2007-12-01), 515-530 0022-3239 135:3<515 2007 135 10957 https://doi.org/10.1007/s10957-007-9239-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9239-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kien B. Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC aut NATIONALLICENCE 700 1- Wong N. Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC aut NATIONALLICENCE 700 1- Yao J. Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 135/3(2007-12-01), 515-530 0022-3239 135:3<515 2007 135 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer