Boundary Value Problems
Volume 2011 (2011), Article ID 767024, 23 pages
doi:10.1155/2011/767024
Research Article

Green's Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions

Svetlana Roman and Artūras Štikonas

Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, Vilnius, LT-08663, Lithuania

Received 1 June 2010; Revised 24 July 2010; Accepted 9 November 2010

Academic Editor: Gennaro Infante

Copyright © 2011 Svetlana Roman and Artūras Štikonas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate a second-order discrete problem with two additional conditions which are described by a pair of linearly independent linear functionals. We have found the solution to this problem and presented a formula and the existence condition of Green's function if the general solution of a homogeneous equation is known. We have obtained the relation between two Green's functions of two nonhomogeneous problems. It allows us to find Green's function for the same equation but with different additional conditions. The obtained results are applied to problems with nonlocal boundary conditions.