A New Method for Proving Existence Theorems for Abstract Hammerstein Equations

Abstract

An abstract Hammerstein equation is an equation of the form $u+KFu=0$. A new method is introduced to prove the existence of a solution of this equation where $K$ and $F$ are 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.