Solvability of boundary-value problems for a linear partial difference equation

Stevo Stevic

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Publication date

January 2017

Publisher

Texas State University

Journal

issn:1072-6691

Abstract

In this article we consider the two-dimensional boundary-value problem $$\displaylines{ d_{m,n}=d_{m-1,n}+f_nd_{m-1,n-1},\quad 1\le n<m,\cr d_{m,0}=a_m,\quad d_{m,m}=b_m,\quad m\in\mathbb{N}, }$$ where $a_m$, $b_m$, $m\in\mathbb{N}$ and $f_n$, $n\in\mathbb{N}$, are complex sequences. Employing recently introduced method of half-lines, it is shown that the boundary-value problem is solvable, by finding an explicit formula for its solution on the domain, the, so called, combinatorial domain. The problem is solved for each complex sequence $f_n$, $n\in\mathbb{N}$, that is, even if some of its members are equal to zero. The main result here extends a recent result in the topic

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Solvability of boundary-value problems for a linear partial difference equation

Abstract

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Solvability of boundary-value problems for a linear partial difference equation

Abstract

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