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| 不动点和一类中立型方程的渐近稳定性 | |
| 引用本文： | 丁黎明,李志祥,原野.不动点和一类中立型方程的渐近稳定性[J].应用数学,2009,22(3). |
| 作者姓名： | 丁黎明 李志祥 原野 |
| 作者单位： | 1. 国防科技大学理学院数学与系统科学系,湖南,长沙,410073;空军雷达学院,湖北,武汉,430010 2. 国防科技大学理学院数学与系统科学系,湖南,长沙,410073 3. 空军工程大学理学院,陕西,西安,710051 |
| 摘 要： | 本文用不动点定理研究了一类中立型泛函微分方程x(t)-P(t)x(t-τ)]′+Q(t)x(t-r(t))=0,t≥t0的零解的渐近稳定性,其中τ∈(0,∞),P,Q∈C(t0,∞),R),r∈C(t0,∞),R+),且当t→∞时t-r(t)→∞.我们讨论了r(t)为常数和不为常数两种情况.所得定理改进和包含了前人已有的结果. |
| 关 键 词： | 不动点 渐近稳定 中立型泛函微分方程 |
Fixed Point and Asymptotic Stability of a Neutral Differential Equation |
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| DING Li-ming,LI Zhi-xiang,YUAN Ye.Fixed Point and Asymptotic Stability of a Neutral Differential Equation[J].Mathematica Applicata,2009,22(3). | |
| Authors: | DING Li-ming LI Zhi-xiang YUAN Ye |
| Abstract: | The asymptotic stability of the zero solution of the scalar neutral functional differential equation x(t)-P(t)x(t-τ)]′+Q(t)x(t-r(t))=0,t≥t_0, is investigated by means of fixed point theory,where τ∈(0,∞),P,Q∈C(t_0,∞),R) and r∈ C(t_0,∞),R+) with t-r(t)→∞ as t→∞.The cases that r(t) is not constant and r(t) is constant are discussed respectively.The obtained theorems improve and generalize previous results. |
| Keywords: | Fixed point Asymptotically stable Neutral functional differential equation |
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