Monotone semilinear equations in Hilbert spaces and applications

Consider a abstract semilinear equation of the formAu+F(u) = 0, where A is amaximalmonotonemap acting into a real Hilbert spaceH, and F is a Lipschitz strongly monotone map on H. Such equations were studied by H. Amann (1982), T. Bartsch (1988), C. Mortici and S. Sburlan (2005, 2006), D. Teodorescu (2005). By standard arguments we can reformulate the problem as a ?xed point equation and prove easier some existence results. Based on these abstract results some applications to partial differential equations are also appended. The method can be adapted for teaching PDE in Technical Universities.