Greens Functional Concept for a Nonlocal Problem

Anahtar Kelimeler:

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Greens Functional Concept for a Nonlocal Problem

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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