Geodesic
Asymptotics of solutions of difference equations with delays
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2016), pp. 66-82

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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
Mots-clés : test equation. 
@article{IVM_2016_7_a7,
     author = {V. V. Malygina and K. M. Chudinov},
     title = {Asymptotics of solutions of difference equations with delays},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {66--82},
     publisher = {mathdoc},
     number = {7},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_7_a7/}
}
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V. V. Malygina; K. M. Chudinov. Asymptotics of solutions of difference equations with delays. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2016), pp. 66-82. http://geodesic.mathdoc.fr/item/IVM_2016_7_a7/