Open AccessGreen’s function for discrete problems with nonlocal boundary conditions
Author(s) -
Svetlana Roman,
Artūras Štikonas
Publication year - 2011
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.2011.sm02
Subject(s) - function (biology) , boundary value problem , homogeneous , green's function , mathematics , order (exchange) , boundary (topology) , relation (database) , mathematical analysis , computer science , combinatorics , finance , database , evolutionary biology , economics , biology
In this article, we investigate an m-order discrete problem with additional conditions which are described by m of linearly independent linear functionals. We have 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 inhomogeneous 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 withnonlocal boundary conditions.
This research was funded by a grant (No. MIP-051/2011) from the Research Council of Lithuania