Solvability of boundary-value problems for a linear partial difference equation
Date
2017-01-14
Authors
Stevic, Stevo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we consider the two-dimensional boundary-value problem
dm,n = dm-1,n + ƒn dm-1,n-1, 1 ≤ n < m,
dm,0 = αm, d m,m = b m, m ∈ ℕ,
where αm, bm, m ∈ ℕ and ƒn, n ∈ 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 ƒn, n ∈ ℕ, that is, even if some of its members are equal to zero. The main result here extends a recent result in the topic.
Description
Keywords
Partial difference equation, Solvable difference equation, Method of half-lines, Combinatorial domain
Citation
Stevic, S. (2017). Solvability of boundary-value problems for a linear partial difference equation. <i>Electronic Journal of Differential Equations, 2017</i>(17), pp. 1-10.
Rights
Attribution 4.0 International