一阶线性差分微分方程振动的充要条件及应用

NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF FIRST ORDER LINEAR DIFFERENCE DIFFERENTIAL EQUATIONS AND APPLIC ATIONS

本文的目的是建立一阶线性差分微分方程 (dx)/(dt)=-sum from i=1 to n p_i(t)x(t-i_x(t)) (1)的所有解关于θ振动的等价条件,然后把所得结果应用于生物自身调节反馈滞后型方程(dN(t))/(dt)=rN(t)[1-(N(t-i))/p] (2)

In this paper,necessary and sufficient conditions for the oscillation of the linear delay differential equation (dx(t))/(dt)=-sum from i=1 to n pi(t)x(t-τ_i(t)) are derived.Then we applied the results to the nonlinear delay differential equation (dx(t))/(dt)=r(t)x(t)[a(t)-sum from i=1 to n b_i(t)x(t-τ_i)(t)] (*' and obtained sufficient conditions for the eventually positive solutions of Ecq. (*) to be oscillatory about K,where K=