New stability conditions for linear difference equations using Bohl-Perron type theorems

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The Bohl-Perron result on exponential dichotomy for a linear difference equation states (under some natural conditions) that if all solutions of the non-homogeneous equation with a bounded right hand side are bounded, then the relevant homogeneous equation is exponentially stable. According to its corollary, if a given equation is close to an exponentially stable comparison equation (the norm of some operator is less than one), then the considered equation is exponentially stable. For a difference equation with several variable delays and coefficients we obtain new exponential stability tests using the above results, representation of solutions and comparison equations with a positive fundamental function.

Original languageEnglish
Pages (from-to)657-675
Number of pages19
JournalJournal of Difference Equations and Applications
Issue number5
StatePublished - 1 May 2011


  • Exponential stability
  • Linear delay difference equations
  • Positive fundamental function

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


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