This article is cited in 6 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.

UDC: 517.55+517.96

MSC: 35R30

Received: 13.12.2015

DOI: 10.17377/smzh.2017.58.218

 English version: Siberian Mathematical Journal, 2017, 58:2, 363–372

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