侯成敏,何延生.具分布偏差变元的中立型微分方程的全局渐近稳定性[J].数学研究及应用,2002,22(4):631~638 |
具分布偏差变元的中立型微分方程的全局渐近稳定性 |
Global Asymptotic Stability of Neutral Differential Equation with Distributed Deviating Arguments |
投稿时间:2000-01-04 |
DOI:10.3770/j.issn:1000-341X.2002.04.022 |
中文关键词: 全局渐近稳定性 分布偏差变元 中立型 |
英文关键词:global asymptotic stability distributed deviating argument neutral. |
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中文摘要: |
本文考虑具分布偏差变元的微分方程[x(t)- Cx(t-r)]′+ f(t,∫-τ0x(t+s)du(s))=0,t≥t0,(1)其中 C,r,τ∈R+且0≤C<1,f(t,x)∈ C([t0,∞],R),xf(t,x)>0,x≠0.通过对方程(1)的非振动解及振动解的渐近性的讨论,获得了方程(1)的全局渐近稳定的充分条件. |
英文摘要: |
In this paper, We consider the differential equation with distributed deviating arguments [x(t)- Cx(t-r)]′+ f(t,∫-τ0x(t+s)du(s))=0,t≥t0.(1) Where C,r,τ ∈ R+ and 0 ≤C < 1,f(t,x) ∈ C(t0,∞],R),xf(t,x) > 0,x≠0. Sufficient conditions for the global asymptotic stability of the zero solution of (1) are obtained by investigating the asymptotic behaviors of the nonoscillatory solutions of (1) and then of the oscillatory solutions. |
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