Authors: | Stević, Stevo | Title: | Solvability of boundary-value problems for a linear partial difference equation | Journal: | Electronic Journal of Differential Equations | Volume: | 2017 | Issue Date: | 1-Jan-2017 | Rank: | M21 | ISSN: | 1072-6691 | Abstract: | In this article we consider the two-dimensional boundary-value problem dm,n = dm−1,n + fndm−1,n−1,1 ≤n < m, dm,0 = am,dm,m = bm, m ∈ ℕ, where am, bm, m ∈ ℕ and fn,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 fn, 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. |
Keywords: | Combinatorial domain | Method of half-lines | Partial difference equation | Solvable difference equation | Publisher: | Texas State University - San Marcos |
Show full item record
SCOPUSTM
Citations
10
checked on Nov 11, 2024
Page view(s)
13
checked on Nov 11, 2024
Google ScholarTM
Check
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.