The solvability of some semilinear perturbed operator equations in infinite dimensional spaces

Abstract

In this paper, the solvability and uniqueness ( of the solution ) of some classes of semilinear operators equations in infinite dimensional space have been considered. The linearity of the semilinear class is of maximal monotone operator perturbed by duality maping, and the nonlinearity are of Leray-Schauder type operator of quasi-positive or satisfying some suitable conditions. The spaces of solvability are real reflexive Banach space or real Hilbert space.