A New Method for Proving Existence Theorems for Abstract Hammerstein Equations

الملخص EN

An abstract Hammerstein equation is an equation of the form u + K F u = 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.