A converse to the Lions-Stampacchia Theorem

Emil Ernst; Michel Théra

Displaying similar documents to “A converse to the Lions-Stampacchia Theorem”

Generalized variational-like inequalities for pseudo-monotone type III operators

Mohammad Chowdhury, Kok-Keong Tan (2008)

Open Mathematics

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Our aim in this paper is mainly to prove some existence results for solutions of generalized variational-like inequalities with (η,h)-pseudo-monotone type III operators defined on non-compact sets in topological vector spaces.

On Pseudo-monotone Operators and Nonlinear Noncoercive Variational Problems on Unbounded Domains.

Rüdiger Landes, Vesa Mustonen (1980)

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Minty variational inequalities and monotone trajectories of differential inclusions.

Crespi, Giovanni P., Rocca, Matteo (2004)

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A converse to the Lions-Stampacchia theorem

Emil Ernst, Michel Théra (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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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.