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.)