Asymptotics of solutions of difference equations with delays

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• 作者：V. V. Malygina ; K. M. Chudinov
• 刊名：Russian Mathematics (Iz VUZ)
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：60
• 期：7
• 页码：56-70
• 全文大小：646 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
• ISSN：1934-810X
• 卷排序：60

文摘

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.Keywordsdelay difference equationstabilitysign-definitenessmonotonicityfundamental solutiontest equation