Greens Functional Concept for a Nonlocal Problem

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Hacettepe Journal of Mathematics and Statistics
Volume:42 Issue:4
Greens Functional Concept for a Nonlocal Problem

Greens Functional Concept for a Nonlocal Problem

Authors : Kemal ÖZEN, Kamil ORUÇOĞLU

Pages : 437-446

View : 59 | Download : 12

Publication Date : 2013-04-01

Article Type : Other Papers

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 : Greens function, loaded differential equation, nonlocal condition, adjointproblem

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