On exponential dichotomy, Bohl-Perron type theorems and stability of difference equations

L. Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

51 Scopus citations

Abstract

For a delay difference equation x(n + 1) = ∑k=-dn A(n, k)x(k) + f(n) in a Banach space the following result is proved: if for any f ∈ lp the solution is x ∈ lp then the solution of the homogeneous equation (f ≡ 0) is exponentially stable. This result is applied to obtain new explicit conditions for exponential stability of a scalar nonautonomous delay difference equation.

Original languageEnglish
Pages (from-to)511-530
Number of pages20
JournalJournal of Mathematical Analysis and Applications
Volume304
Issue number2
DOIs
StatePublished - 15 Apr 2005

Keywords

  • Difference equations
  • Explicit stability conditions
  • Exponential dichotomy
  • Exponential stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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