Green and Generalized Green’s Functionals of Linear Local and Nonlocal Problems for Ordinary Integro-differential Equations

Abstract

The author presents a study of a linear nonhomogeneous multipoint problem through study of an adjoint system in the form of three integro-algebraic equations. The paper is organised as follows: after preliminaries, the special adjoint form is introduced. Solvability conditions are considered and the Greens functional and a generalized version is described. There is a discussion of the relationship of the Greens functional with Greens functions and Cauchy functions and the paper concludes with a review of applications.