Oscillation and Other Properties of Linear Impulsive and Nonimpulsive Delay Equations

L. Berezansky, E. Braverman

Research output: Contribution to journalArticlepeer-review

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Abstract

Many of the oscillation results for linear impulsive equations were justified by the following scheme. First, the equivalence of the oscillation of the impulsive equation and some specially constructed nonimpulsive equation was established; further, on the base of well-known results for the nonimpulsive case, the oscillation of the impulsive equation was analyzed. In the present paper, we prove the "oscillation equivalence" result for a linear impulsive equation with a distributed delay and discuss the possibility to expand this approach to the other properties of impulsive equations, for example, stability and asymptotic behavior. In addition, a linear impulsive equation of the second order is considered.

Original languageEnglish
Pages (from-to)1025-1030
Number of pages6
JournalApplied Mathematics Letters
Volume16
Issue number7
DOIs
StatePublished - 1 Jan 2003

Keywords

  • Distributed delay
  • Impulses
  • Nonoscillation
  • Oscillation

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