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In this paper we show that a linear variational inequality over an infinite dimensional real Hilbert space admits solutions for every nonempty bounded closed and convex set, if and only if the linear operator involved in the variational inequality is pseudo-monotone in the sense of Brezis.
@article{COCV_2009__15_4_810_0,
author = {Ernst, Emil and Th\'era, Michel},
title = {A converse to the {Lions-Stampacchia} theorem},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {810--817},
publisher = {EDP-Sciences},
volume = {15},
number = {4},
year = {2009},
doi = {10.1051/cocv:2008054},
mrnumber = {2567246},
zbl = {1176.47050},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008054/}
}
TY - JOUR AU - Ernst, Emil AU - Théra, Michel TI - A converse to the Lions-Stampacchia theorem JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 810 EP - 817 VL - 15 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008054/ DO - 10.1051/cocv:2008054 LA - en ID - COCV_2009__15_4_810_0 ER -
%0 Journal Article %A Ernst, Emil %A Théra, Michel %T A converse to the Lions-Stampacchia theorem %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 810-817 %V 15 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008054/ %R 10.1051/cocv:2008054 %G en %F COCV_2009__15_4_810_0
Ernst, Emil; Théra, Michel. A converse to the Lions-Stampacchia theorem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 4, pp. 810-817. doi: 10.1051/cocv:2008054
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