| 一类二阶非线性微分方程零解的全局渐近稳定性 |
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| 引用本文： | 张红玲,裴新年,李宝毅. 一类二阶非线性微分方程零解的全局渐近稳定性[J]. 天津师范大学学报(自然科学版), 2011, 31(3): 13-16,21 |
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| 作者姓名： | 张红玲 裴新年 李宝毅 |
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| 作者单位： | 1. 天津师范大学 数学科学学院,天津,300387
2. 中共天津市委党校 基础课教研部,天津,300191 |
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| 摘 要： | 研究一类二阶非线性微分方程零解的全局渐近稳定性,证明了该系统所有正半轨都是正向有界的,从而得到该系统零解全局渐近稳定的一些条件.推广了相关文献的某些结论,之前较多结果都可由本研究结果推出.
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| 关 键 词： | 二阶非线性微分方程 零解 全局渐近稳定性 正半轨 正向有界 |
Global asymptotic stability of zero solution for a class of second order nonlinear differential equations |
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| ZHANG Hongling,PEI Xinnian,LI Baoyi. Global asymptotic stability of zero solution for a class of second order nonlinear differential equations[J]. Journal of Tianjin Normal University(Natural Science Edition), 2011, 31(3): 13-16,21 |
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| Authors: | ZHANG Hongling PEI Xinnian LI Baoyi |
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| Affiliation: | ZHANG Hongling1,PEI Xinnian2,LI Baoyi11.College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China,2.Department of Basic Courses,Party School of CPC Tianjin Municipal Committee,Tianjin 300191 |
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| Abstract: | The global asymptotic stability of the zero solution for a class of second order nonlinear differential equations is studied.Some sufficient conditions and a necessary condition are obtained by proving that all the positive semi-orbits of the system are positively bounded.Some results of relevant literatures are extended and some previous results can be obtained from this paper's results. |
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| Keywords: | second order nonlinear differential equations zero solution global asymptotic stability positive semi-orbit positively bounded |
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