Green’s function for discrete problems with nonlocal boundary conditions

Svetlana Roman; Artūras Štikonas

doi:10.15388/LMR.2011.sm02

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.

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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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