On oscillation of a differential equation with infinite number of delays

L. Berezansky, E. Braverman

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

For a scalar delay differential equation ẋ(t) + ∑k=1ak(t)x(hk(t)) = 0 (hk(t) ≤ t) a connection between the following four properties is established: - non-oscillation of this equation - non-oscillation of the corresponding differential inequality - positiveness of the fundamental function - existence of a non-negative solution for a certain explicitly constructed nonlinear integral inequality. Explicit non-oscillation and oscillation conditions, comparison theorems and a criterion of the existence of a positive solution are presented for this equation.

Original languageEnglish
Pages (from-to)803-816
Number of pages14
JournalZeitschrift fur Analysis und ihre Anwendung
Volume21
Issue number3
DOIs
StatePublished - 1 Jan 2002

Keywords

  • Delay differential equations
  • Infinite number of delays
  • Non-oscillation
  • Oscillation

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