Existence, Uniqueness and Validation of Parameter Imbedding Equations for Nonlinear Fredholm Integral Equations.

摘要

A parameter imbedding method for nonlinear Fredholm integral equations produces a Cauchy system involving the solution of the integral equation and an associated resolvent kernel. For such Cauchy systems sufficient conditions are given to guarantee local existence and uniqueness of solutions. A Picard-type theorem utilizing a Lipschitz condition is obtained. This result then yields the validation of the Cauchy system. (ERA citation 04:038030)