Linearized oscillation theory for a nonlinear delay impulsive equation

[摘要] For a scalar nonlinear impulsive delay differential equation (y) over dot (t) + [GRAPHICS] r(k)(t)f(k)[y(h(k)(t))] = 0, t not equal tau(j), y(tau(j)) = y(tau(j)(-))) with r(k)(t) greater than or equal to 0, h(k)(t) less than or equal to t, lim(j-->infinity) tau(j) = infinity, Such an auxiliary linear impulsive delay differential equation (x) over dot (t) [GRAPHICS] r(k)(t)a(k)(t)x(h(k)(t)) = 0, x(tau(j)) = b(j)x(tau(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. (C) 2003 Elsevier B.V. All rights reserved.

[发布日期] 2003-12-15

[关键词] oscillation;delay impulsive equations;linearization