Browder–Minty theorem

In mathematics, the Browder–Minty theorem states that a bounded, continuous, coercive and monotone function T from a real, separable reflexive Banach space X into its continuous dual space X is automatically surjective. That is, for each continuous linear functional g  X, there exists a solution u  X of the equation T(u) = g. (Note that T itself is not required to be a linear map.)

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