Approximation of Solutions of Nonlinear Integral Equations of Hammerstein Type

Abstract EN

Suppose that H is a real Hilbert space and F,K:H→H are bounded monotone maps with D(K)=D(F)=H.

Let u* denote a solution of the Hammerstein equation u+KFu=0.

An explicit iteration process is shown to converge strongly to u*.

No invertibility or continuity assumption is imposed on K and the operator F is not restricted to be angle-bounded.

Our result is a significant improvement on the Galerkin method of Brézis and Browder.