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

 dc.contributor.author Stevic, Stevo dc.date.accessioned 2022-03-16T21:32:53Z dc.date.available 2022-03-16T21:32:53Z dc.date.issued 2017-01-14 dc.description.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. dc.description.department Mathematics dc.format Text dc.format.extent 10 pages dc.format.medium 1 file (.pdf) dc.identifier.citation Stevic, S. (2017). Solvability of boundary-value problems for a linear partial difference equation. Electronic Journal of Differential Equations, 2017(17), pp. 1-10. dc.identifier.issn 1072-6691 dc.identifier.uri https://hdl.handle.net/10877/15522 dc.language.iso en dc.publisher Texas State University, Department of Mathematics dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.source Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. dc.subject Partial difference equation dc.subject Solvable difference equation dc.subject Method of half-lines dc.subject Combinatorial domain dc.title Solvability of boundary-value problems for a linear partial difference equation dc.type Article

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