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.
C. E. Chidume. C. O. Chidume. Ma’aruf Shehu Minjibir. "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