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Sibirsk. Mat. Zh., 2017, Volume 58, Number 2, Pages 468–480 (Mi smj2873)  

This article is cited in 2 scientific papers (total in 2 papers)

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

T. I. Yakovleva

Siberian Federal University, Krasnoyarsk, Russia

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.)


DOI: https://doi.org/10.17377/smzh.2017.58.218

Full text: PDF file (320 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:2, 363–372

Bibliographic databases:

UDC: 517.55+517.96
MSC: 35R30
Received: 13.12.2015

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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\paper Well-posedness of the Cauchy problem for multidimensional difference equations in rational cones
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\pages 468--480
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\pages 363--372
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. K. Leinartas, T. I. Yakovleva, “The Cauchy problem for multidimensional difference equations and the preservation of the hierarchy of generating functions of its solutions”, Zhurn. SFU. Ser. Matem. i fiz., 11:6 (2018), 712–722  mathnet  crossref
    2. E. K. Leinartas, T. I. Yakovleva, “On formal solutions of hormander's initial-boundary value problem in the class of laurent series”, J. Sib. Fed. Univ.-Math. Phys., 11:3 (2018), 278–285  mathnet  crossref  mathscinet  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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