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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 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
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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
Received: 19.12.2014
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 7, Pages 56–70
DOI: https://doi.org/10.3103/S1066369X16070082
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: Russian
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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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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