A New Method for Proving Existence Theorems for Abstract Hammerstein Equations

Abstract

An abstract Hammerstein equation is an equation of the formu+KFu=0. Anew methodis introduced to prove the existence of a solution of this equation whereKandFare nonlinear accretive (monotone) operators. The method does not involve the complicated technique of factorizing a linear map via a Hilbert space and does not involve the use of deep variational techniques.