Greens Functional Concept for a Nonlocal Problem

Kemal Özen; Kamil Oruçoğlu

Greens Functional Concept for a Nonlocal Problem

Year 2013, Volume: 42 Issue: 4, 437 - 446, 01.04.2013

Abstract

In this work, by Green’s functional concept, in order to obtain Green’ssolution we concentrate on a new constructive technique by which alinear completely nonhomogeneous nonlocal problem for a second-orderloaded differential equation with generally variable coefficients satisfying some general properties such as p-integrability and boundedness istransformed into one and only one integral equation. A system of threeintegro-algebraic equations called the special adjoint system is obtainedfor this problem. A solution of this special adjoint system is Green’sfunctional which enables us to determine Green’s function and Green’ssolution for the problem. Two illustrative applications are provided.

Keywords

Green’s function; loaded differential equation; nonlocal condition; adjointproblem.

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