Approximation of Solutions of Nonlinear Integral Equations of Hammerstein Type

摘要

Suppose thatHis a real Hilbert space andF,K:H→Hare bounded monotone maps withD(K)=D(F)=H. Letu*denote a solution of the Hammerstein equationu+KFu=0. An explicititeration processis shown to converge strongly tou*. No invertibility or continuity assumption is imposed onKand the operatorFis not restricted to be angle-bounded. Our result is a significant improvement on the Galerkin method of Brézis and Browder.