Green's functions for discrete \(m\)th-order problems
type: Item
instance of: scholarly article
title: Green's functions for discrete \(m\)th-order problems
zbMATH Open document ID: 1264.39008
author: Svetlana Roman
author: A. Štikonas
published in: Lithuanian Mathematical Journal
publication date: 2013-03-21T00:00:00Z
review text: This paper concerns the \(m\)th-order linear ordinary difference equation \(a^m_iu_{i+m} +\dots + a^2_iu_{i+2} + a^1_iu_{i+1} + a^0_iu_i = f_i,\) \(i = \overline{0, n-m}\), where \(0 \leq n\in \mathbb{N}\), \(m = \overline{0, n}\), and \(a^m_i\), \(a^0_i\not= 0\). The expression of the solution to the equation is given under additional conditions: \(\langle L_1, u\rangle= g_1\in \mathbb{K},\dots, \langle L_m, u\rangle= g_m\in \mathbb{K}\), where \(L_1,\dots,L_m\) are linearly independent functionals. Moreover, a discrete Green function is defined, and the Green function is constructed for the equation. Applications to two problems with nonlocal boundary conditions are also given.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B27
Mathematics Subject Classification ID: 39A06
zbMATH DE Number: 6147479
zbMATH Keywords: nonlocal boundary conditions
zbMATH Keywords: linear ordinary difference equation
zbMATH Keywords: discrete Green's function
reviewed by: Ti-Jun Xiao
MaRDI profile type: Publication
full work available at URL: s10986-012-9177-1
OpenAlex ID: W2082540654
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DOI: 10.1007/S10986-012-9177-1
description: scientific article; zbMATH DE number 6147479