A New Method for Proving Existence Theorems for Abstract Hammerstein Equations - C. E. Chidume; C. O. Chidume; Ma’aruf Shehu Minjibir (Abstract and Applied Analysis)
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.