A converse to the Lions-Stampacchia Theorem
Aix-Marseille Univ, UMR6632, Marseille, 13397, France. Emil.Ernst@univ-cezanne.fr
2 XLIM (UMR-CNRS ) and Université de Limoges, 123 Avenue A. Thomas, 87060 Limoges Cedex, France. email@example.com
Revised: 14 February 2008
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.
Mathematics Subject Classification: 47H05 / 52A41 / 39B82
Key words: Lions-Stampacchia Theorem / variational inequality / pseudo-monotone operator
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