Electron. J. Differential Equations,
Vol. 2017 (2017), No. 17, pp. 110.
Solvability of boundaryvalue problems for a linear partial difference equation
Stevo Stevic
Abstract:
In this article we consider the twodimensional boundaryvalue problem
where
,
,
and
,
,
are complex sequences. Employing recently introduced method of halflines,
it is shown that the boundaryvalue 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 halflines; combinatorial domain.
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Stevo Stevic
Mathematical Institute of the Serbian Academy of Sciences
Knez Mihailova 36/III,
11000 Beograd, Serbia
email: sstevic@ptt.rs

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