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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 2, Pages 468–480
DOI: https://doi.org/10.17377/smzh.2017.58.218 (Mi smj2873) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Well-posedness of the Cauchy problem for multidimensional difference equations in rational cones

T. I. Yakovleva

Siberian Federal University, Krasnoyarsk, Russia
Full-text PDF (320 kB) Citations (6)
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DOI: https://doi.org/10.17377/smzh.2017.58.218
Abstract: The Cauchy problem is studied for a multidimensional difference equation in a class of functions defined at the integer points of a rational cone. We give an easy-to-check condition on the coefficients of the characteristic polynomial of the equation sufficient for solvability of the problem. A multidimensional analog of the condition ensuring stability of the Cauchy problem is stated on using the notion of amoeba of an algebraic hypersurface.
Keywords: multidimensional difference equation, well-posedness of the Cauchy problem, rational cone.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.Y26.31.0006
НШ-9149.2016.1
The author was supported by the Government of the Russian Federation (Grant 14.Y26.31.0006) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-9149.2016.1.)
Received: 13.12.2015
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 2, Pages 363–372
DOI: https://doi.org/10.1134/S0037446617020185
Bibliographic databases:
Document Type: Article
UDC: 517.55+517.96
MSC: 35R30
Language: Russian
Citation: T. I. Yakovleva, “Well-posedness of the Cauchy problem for multidimensional difference equations in rational cones”, Sibirsk. Mat. Zh., 58:2 (2017), 468–480; Siberian Math. J., 58:2 (2017), 363–372
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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