Integral solution of a class of nonlinear integral equations

摘要

This paper is concerned with the existence of integral solutions to a general nonlinear integral equationx(t)=f1(t,x(ϕ1(t)))+f2t,∫0ϕ2(t)k(t,s)f3(s,x(ϕ3(s)))ds,t∈R+.With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we establish a new and general existence theorem for the nonlinear functional integral equation. Moreover, an example, which can not be treated by the related theorems in [5], [20], [22], is given to illustrate the new existence theorem.