On Monotone Methods And The Solution Of Nonlinear Integral Equations Of Hammerstein Type

This paper is an introduction, with historical background, to the use of monotone mapping methods in the solution of nonlinear integral equations of Hammerstein type.Chapters I and II contain the necessary historical background.Chapter III presents a survey of the work done in the period 1960 to 1975 by the principal investigators in this area, i.e. G. J. Minty and Felix Browder (along with his collaborators). The development of the use of monotone mapping methods is followed through its generalizations; first for the Hilbert space case and then to the striking results obtained by F. Browder and H. Brezis in 1972.