| Asymptotic Stability of Neutral Differential Equations with Unbounded Delay |
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| 作者姓名： | 叶海平 高国柱 |
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| 作者单位： | YE Hai-ping，GAO Guo-zhuDepartment of Applied Mathematics，Dong Hua University，Shanghai，200051 |
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| 基金项目： | theScienceFoundationofDongHuaUniversity |
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| 摘 要： | ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｎｅｕｔｒａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｗｉｔｈｐｏｓｉ ｔｉｖｅａｎｄｎｅｇａｔｉｖｅｃｏｅｆｆｉｃｉｅｎｔｓａｎｄｕｎｂｏｕｎｄｅｄｄｅｌａｙｄｄｔｘ(ｔ) -Ｐ(ｔ)ｘ(ｈ(ｔ) ) ]+Ｑ(ｔ)ｘ(ｑ(ｔ) ) -Ｒ(ｔ)ｘ(ｒ(ｔ) ) =0 ,ｔ≥ｔ0 . (1)Ｉｔｉｓａｓｓｕｍｅｄｔｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒｔｈａｔ(ａ)Ｐ(ｔ) ∈Ｃ(ｔ0 ,∞ ) ,Ｒ) ,Ｑ(ｔ) ,Ｒ(ｔ) ∈Ｃ(ｔ0 ,∞ ) ,Ｒ+ ) .(ｂ)ｈ ,ｑ ,ｒ:ｔ0 ,∞ )→Ｒａｒｅｃｏｎｔｉｎ…
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Asymptotic Stability of Neutral Differential Equations with Unbounded Delay |
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| YE Hai-ping,GAO Guo-zhu.Asymptotic Stability of Neutral Differential Equations with Unbounded Delay[J].Journal of Donghua University,2002,19(3). |
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| Authors: | YE Hai-ping GAO Guo-zhu |
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| Institution: | Department of Applied Mathematics,Dong Hua University,Shanghai,200051 |
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| Abstract: | Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt x(t)- P(t)x(h(t))] + Q(t)x(q(t)) -R(t)x(r(t))= 0, t ≥ t0,where P(t)∈ C(t0, ∞), R), Q(t), R(t) ∈ C(t0,∞ ), R+ ), and h, q, r: t0, ∞ ) → R are continuously differentiable and strictly increasing, h( t) ＜ t, q( t) ＜t, r(t) ＜ t for all t ≥ t0. In this paper, the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable. |
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| Keywords: | neutral equation uniform stability asymptotic stability unbounded delay |
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