考虑变系数高阶中立型微分方程(NDDE)d^n/(dt^n)[y(t)+p(t)y(t-τ)]+sum from n=1 to ∞q^i(t)y(t-σ_i)=0 (1)其中p(t)、g_i(t)都是区间[T,∞)上连续的实值函数.p(t)有界,q_i(t)≥0(i=1,2,···,m)且至少有一个q_i(t)最...考虑变系数高阶中立型微分方程(NDDE)d^n/(dt^n)[y(t)+p(t)y(t-τ)]+sum from n=1 to ∞q^i(t)y(t-σ_i)=0 (1)其中p(t)、g_i(t)都是区间[T,∞)上连续的实值函数.p(t)有界,q_i(t)≥0(i=1,2,···,m)且至少有一个q_i(t)最终大于某一任意小的正数.τ≥0,σ_i≥0.m≥1,n≥1均为正整数. 本文研究了方程(1)在p(t)≥一1及p(t)≤-1等情况下解的渐近性和振动性,获得了一系列使解振动的充分条件.特别,p(t)有时可以是变号函数.展开更多
Consider the high order neutral differential equation(y(t) +p(t)y(h(t)))^(n)+q(t)y(g(t))=0, (1)where p(t), q(t), h(t) and g(t)∈ C[t_0,+∞);q(t)>0;h(t)→∞, g (t)→∞ as t→∞;n≥2.The author studies the oscillatio...Consider the high order neutral differential equation(y(t) +p(t)y(h(t)))^(n)+q(t)y(g(t))=0, (1)where p(t), q(t), h(t) and g(t)∈ C[t_0,+∞);q(t)>0;h(t)→∞, g (t)→∞ as t→∞;n≥2.The author studies the oscillation of (1) when p(t) has an arbitrarily large zero, and obtainssome sufficient conditions.展开更多
基金This project is supported by the State Natural Science Fund of China
文摘考虑变系数高阶中立型微分方程(NDDE)d^n/(dt^n)[y(t)+p(t)y(t-τ)]+sum from n=1 to ∞q^i(t)y(t-σ_i)=0 (1)其中p(t)、g_i(t)都是区间[T,∞)上连续的实值函数.p(t)有界,q_i(t)≥0(i=1,2,···,m)且至少有一个q_i(t)最终大于某一任意小的正数.τ≥0,σ_i≥0.m≥1,n≥1均为正整数. 本文研究了方程(1)在p(t)≥一1及p(t)≤-1等情况下解的渐近性和振动性,获得了一系列使解振动的充分条件.特别,p(t)有时可以是变号函数.
文摘Consider the high order neutral differential equation(y(t) +p(t)y(h(t)))^(n)+q(t)y(g(t))=0, (1)where p(t), q(t), h(t) and g(t)∈ C[t_0,+∞);q(t)>0;h(t)→∞, g (t)→∞ as t→∞;n≥2.The author studies the oscillation of (1) when p(t) has an arbitrarily large zero, and obtainssome sufficient conditions.
