Green’s functional concept for a nonlocal problem

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