In this article we consider the two-dimensional boundary-value problem
where , , and , , 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 , , that is, even if some of its members are equal to zero. The main result here extends a recent result in the topic.
Submitted October 23, 2016. Published January 14, 2017.
Math Subject Classifications: 39A14, 39A06.
Key Words: Partial difference equation; solvable difference equation; method of half-lines; combinatorial domain.
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| Stevo Stevic |
Mathematical Institute of the Serbian Academy of Sciences
Knez Mihailova 36/III, 11000 Beograd, Serbia
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