An abstract Hammerstein equation is an equation of the form . A new method is introduced to prove the existence of a solution of this equation where and 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.
"A New Method for Proving Existence Theorems for Abstract Hammerstein Equations." Abstr. Appl. Anal. 2015 1 - 7, 2015. https://doi.org/10.1155/2015/627260