Linearized oscillation theory for a nonlinear delay impulsive equation

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


For a scalar nonlinear impulsive delay differential equation ẏ(t) + ∑mk=1 rk(t)fk [y(hk(t))] = 0, t ≠ τj, sp=0.5>y(τj) =Ij(y(τ-j)) with rk(t) ≥ 0,hk(t) ≤ t, limj→∞ τj = ∞, such an auxiliary linear impulsive delay differential equation x(t) + ∑mk=1 rk(t)ak(t)x (hk(t)) = 0, x(τj) = bj x(τ-j) is constructed that oscillation (nonoscillation) of the nonlinear equation can be deduced from the corresponding properties of the linear equation. Coefficients rk(t) and delays are not assumed to be continuous. Explicit oscillation and nonoscillation conditions are established for some nonlinear impulsive models of population dynamics, such as the impulsive logistic equation and the impulsive generalized Lasota-Wazewska equation which describes the survival of red blood cells. It is noted that unlike nonimpulsive delay logistic equations a solution of a delay impulsive logistic equation may become negative.

Original languageEnglish
Pages (from-to)477-495
Number of pages19
JournalJournal of Computational and Applied Mathematics
Issue number2
StatePublished - 15 Dec 2003


  • Delay impulsive equations
  • Linearization
  • Oscillation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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