Green’s function for discrete problems with nonlocal boundary conditions
Articles
Svetlana Roman
Vilnius University
https://orcid.org/0000-0002-4479-6560
Artūras Štikonas
Vilnius University
https://orcid.org/0000-0002-5872-5501
Published 2011-12-15
https://doi.org/10.15388/LMR.2011.sm02
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Keywords

m-order discrete problem
Green’s function
nonlocal boundary conditions

How to Cite

Roman S. and Štikonas A. (2011) “Green’s function for discrete problems with nonlocal boundary conditions”, Lietuvos matematikos rinkinys, 52(proc. LMS), pp. 291-296. doi: 10.15388/LMR.2011.sm02.

Abstract

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 with
nonlocal boundary conditions.

This research was funded by a grant (No. MIP-051/2011) from the Research Council of Lithuania

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