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functional analysis - Minty-Browder theorem - Mathematics Stack Exchange You can find this exact result in the book "Linear and Nonlinear Functional Analysis with Applications" by Ciarlet, see Theorem 9 14 Also in the german book "Nichtlineare Funktionalanalysis" by Ruzicka and in the following lecture notes, Theorem 9 13 Note that for a monotone operator demicontinuity and hemicontinuity are equivalent, see Proposition 9 11 in the lecture notes So you find a