## 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