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 J. Sib. Fed. Univ. Math. Phys., 2020, Volume 13, Issue 2, Pages 187–196 (Mi jsfu830)

The Cauchy problem for multidimensional difference equations in lattice cones

Alexander P. Lyapinab, Sreelatha Chandragirib

a Lesosibirsk Pedagogical Institute — branch of SFU, Lesosibirsk, Russian Federation
b Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: We consider a variant of the Cauchy problem for a multidimensional difference equation with constant coefficients, which connected with a lattice path problem in enumerative combinatorial analysis. We obtained a formula in which generating function of the solution to the Cauchy problem is expressed in terms of generating functions of the Cauchy data and a formula expressing solution to the Cauchy problem through its fundamental solution and Cauchy data.

Keywords: difference equation, fundamental solution, generating function, Dyck paths.

 Funding Agency This work of author was financed by the PhD SibFU grant for support of scientific research no. 14.

DOI: https://doi.org/10.17516/1997-1397-2020-13-2-187-196

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Bibliographic databases:

UDC: 517.55+517.962.26
Accepted: 03.02.2020
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Citation: Alexander P. Lyapin, Sreelatha Chandragiri, “The Cauchy problem for multidimensional difference equations in lattice cones”, J. Sib. Fed. Univ. Math. Phys., 13:2 (2020), 187–196

Citation in format AMSBIB
\Bibitem{LyaCha20} \by Alexander~P.~Lyapin, Sreelatha~Chandragiri \paper The Cauchy problem for multidimensional difference equations in lattice cones \jour J. Sib. Fed. Univ. Math. Phys. \yr 2020 \vol 13 \issue 2 \pages 187--196 \mathnet{http://mi.mathnet.ru/jsfu830} \crossref{https://doi.org/10.17516/1997-1397-2020-13-2-187-196} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000526181200006}