A Procedure for Factoring and Solving Nonlocal Boundary Value Problems for a Type of Linear Integro-Differential Equations

Abstract

The aim of this article is to present a procedure for the factorization and exact solution of boundary value problems for a class of n-th order linear Fredholm integro-differential equations with multipoint and integral boundary conditions. We use the theory of the extensions of linear operators in Banach spaces and establish conditions for the decomposition of the integro-differential operator into two lower-order integro-differential operators. We also create solvability criteria and derive the unique solution in closed form. Two example problems for an ordinary and a partial intergro-differential equation respectively are solved.

Keywords

• integro-differential equations
• factorization
• nonlocal boundary value problems
• integral conditions
• multipoint conditions
• decomposition of operators