New general solution to a nonlinear Fredholm integro-differential equation

Abstract

Partition Δₙ of the interval [0, T] into N parts and introduction of additional parameters and new unknown functions on subintervals reduce a nonlinear Fredholm integro-differential equation to the special Cauchy problems for a system of nonlinear integro-differential equations with parameters. Conditions for the existence of a unique solution to the latter problem are obtained. Employing this solution we construct a Δₙ general solution to the nonlinear Fredholm integro-differential equation. Properties of the Δₙ general solution and its application to a nonlinear boundary value problem for the considered equation are discussed.