## Abstract

For a scalar nonlinear impulsive delay differential equation ẏ(t) + ∑^{m}_{k=1} r_{k}(t)f_{k} [y(h_{k}(t))] = 0, t ≠ τ_{j}, sp=0.5>y(τ_{j}) =I_{j}(y(τ^{-}_{j})) with r_{k}(t) ≥ 0,h_{k}(t) ≤ t, lim_{j→∞} τ_{j} = ∞, such an auxiliary linear impulsive delay differential equation x(t) + ∑^{m}_{k=1} r_{k}(t)a_{k}(t)x (h_{k}(t)) = 0, x(τ_{j}) = b_{j} x(τ^{-}_{j}) is constructed that oscillation (nonoscillation) of the nonlinear equation can be deduced from the corresponding properties of the linear equation. Coefficients r_{k}(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 language | English |
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Pages (from-to) | 477-495 |

Number of pages | 19 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 161 |

Issue number | 2 |

DOIs | |

State | Published - 15 Dec 2003 |

## Keywords

- Delay impulsive equations
- Linearization
- Oscillation

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics