A converse to the Lions-Stampacchia Theorem
Emil Ernst, Michel A. Théra · ESAIM Control Optimisation and Calculus of Variations · 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.