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A contractive method for a semilinear equation in Hilbert spaces. (English) Zbl 1150.47351

Summary: In this note, we establish an existence and uniqueness result for the semilinear equation \(Au+F(u)=f\), where \(A\) is a linear maximal monotone and strongly positive operator and the nonlinearity \(F\) is a Lipschitz operator.

MSC:

47H06 Nonlinear accretive operators, dissipative operators, etc.
47H10 Fixed-point theorems
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