Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 121, pp. 1-12.

Title: Green's functional for second-order linear differential equation with
       nonlocal conditions
  
Authors: Kamil Orucoglu (Istanbul Technical Univ., Turkey)
         Kemal Ozen     (Istanbul Technical Univ., Turkey)

Abstract:
 In this work, we present a new constructive technique which is based
 on Green's functional concept. According to this technique, a linear
 completely nonhomogeneous nonlocal problem for a second-order ordinary
 differential equation is reduced to one and only one integral equation
 in order to identify the Green's solution. The coefficients of
 the equation are assumed to be generally variable nonsmooth functions
 satisfying some general properties such as p-integrability and boundedness.
 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 the Green's
 function and the Green's solution for the problem. Some illustrative
 applications and comparisons are provided with some known results.

Submitted February 23, 2012. Published July 19, 2012.
Math Subject Classifications: 34A30, 34B05, 34B10, 34B27, 45A05.
Key Words: Green's function; nonlocal boundary conditions; 
           nonsmooth coefficient; adjoint problem.