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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 7, Pages 66–82 (Mi ivm9135)  

Asymptotics of solutions of difference equations with delays

V. V. Malygina, K. M. Chudinov

Perm National Research Polytechnic University, 29 Komsomol'skii Ave., Perm, 614990 Russia

Abstract: We consider a linear scalar difference equation with several variable delays and constant coefficients. The coefficients and maximum admissible values of delays are supposed to be the set of parameters that define a family of equations of the investigated class. We obtain effective necessary and sufficient conditions of the uniform and exponential stability of solutions to all equations of the family, as well as the conditions of the sign-definiteness and monotonicity of stable solutions.

Keywords: delay difference equation, stability, sign-definiteness, monotonicity, fundamental solution, test equation.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 2014/152, проект 1890
Russian Foundation for Basic Research 13-01-96050


Full text: PDF file (262 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:7, 56–70

Bibliographic databases:

UDC: 517.929
Received: 19.12.2014

Citation: V. V. Malygina, K. M. Chudinov, “Asymptotics of solutions of difference equations with delays”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 7, 66–82; Russian Math. (Iz. VUZ), 60:7 (2016), 56–70

Citation in format AMSBIB
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\by V.~V.~Malygina, K.~M.~Chudinov
\paper Asymptotics of solutions of difference equations with delays
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 7
\pages 66--82
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\transl
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 7
\pages 56--70
\crossref{https://doi.org/10.3103/S1066369X16070082}
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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