Linearized oscillation theory for a nonlinear equation with a distributed delay

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We obtain linearized oscillation theorems for the equation with distributed delays (1)over(x, ̇) (t) + underover(∑, k = 1, m) rk (t) ∫- ∞t fk (x (s)) ds Rk (t, s) = 0 . The results are applied to logistic, Lasota-Wazewska and Nicholson's blowflies equations with a distributed delay. In addition, the "Mean Value Theorem" is proved which claims that a solution of (1) also satisfies the linear equation with a variable concentrated delay over(x, ̇) (t) + (underover(∑, k = 1, m) rk (t) fkk (t))) x (g (t)) = 0 .

Original languageEnglish
Pages (from-to)287-304
Number of pages18
JournalMathematical and Computer Modelling
Volume48
Issue number1-2
DOIs
StatePublished - 1 Jul 2008

Keywords

  • Distributed delay
  • Lasota-Wazewska model
  • Linearization
  • Logistic equation
  • Nicholson's blowflies equation
  • Oscillation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computer Science Applications

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