Green's Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions
Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, Vilnius, LT-08663, Lithuania
Boundary Value Problems 2011, 2011:767024 doi:10.1155/2011/767024Published: 24 November 2010
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.