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Let the nonlinear operator $ F:H\to H$ be weakly continuous on the separable Hilbert space $ H$ , i.e., if $ x_n\to x_0$ weakly then $ F(x_n)\to F(x_0)$ weakly in $ H$ . This nonlinear operator also admits local Lipschitz continuity in the strong sense. Now, consider a sequence $ x_n(t)\in C(0,T;H)$ weakly convergent inRead more