A Transformation Technique for Boundary Value Problem with Linear Nonlocal Condition by Green's Functional Concept

摘要

In this work, with the aim of determining Green's solution we propose a constructive technique by which a linear or nonlinear boundary value problem involving linear nonlocal integral condition for a first-order ordinary integro-differential equation with generally nonsmooth coefficients satisfying some general properties such as p-integrability and boundedness is generally transformed into an integral equation. A system of two integro-algebraic equations, called "the special adjoint system" corresponding to an integral equation in the form of unique equation, is constructed for this problem. A solution of this special adjoint system is Green's functional which enables us to determine Green's function for the problem. Two illustrative applications are provided with known results.