An iterative method for solving nonlinear integral equations of Hammerstein type

Suppose H   is a real Hilbert space and F,K:H→H are continuous bounded monotone maps with D(K)=D(F)=HD(K)=D(F)=H. Assume that the Hammerstein equation u+KFu=0u+KFu=0 has a solution. An explicit iteration process is proved to converge strongly to a solution of this equation. No invertibility assumption is imposed on K and the operator F is not restricted to be angle-bounded. Our theorem complements the Galerkin method of Brézis and Browder to provide methods for approximating solutions of nonlinear integral equations of Hammerstein type.