摘要
考虑中立型时滞微分方程d^2/dt^2[y(t)+P(t)y(t-τ)]+Q(t)y(t-σ)=0,t≥t_0 (1)其中P,Q∈C([t_0,+∞),R),,τ和σ是非负实数.我们证明了下列定理: 定理1 设0≤P(t)≤1,Q(t)≥0,且∫_(t_0)^(+∞)Q(s)[1-P(s-σ)]ds=+∞则方程(1)的一切解振动. 定理2 设P(t)≡P≥0,∫_(t_0)^(+∞)Q(s)ds=+∞,则方程(1)的一切可微解的导数振动.
Consider the second order neutral delay differential equation (1) where P, Q∈C([t_0,+∞), R), both τ and σ are nonnegative real number. We obtain the following theorems:Theorem 1 If 0≤P(t)≤1, Q(t)≥1 then all solutions of (1)are oscillatory. Theorem 2 If then derivatives of all differentiable solutions of (1)are oscillatory.
出处
《山东师范大学学报（自然科学版）》
CAS
1990年第4期20-23,19,共5页
Journal of Shandong Normal University(Natural Science)
关键词
中立型方程
振动性
时滞
微分方程
neutral equation
oscillation
delay differential equation
