| 一类二阶变系数微分方程基本解组的渐近逼近式与解的渐近性态 |
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| 引用本文： | 张建军,贾永录,肖辞元.一类二阶变系数微分方程基本解组的渐近逼近式与解的渐近性态[J].西华师范大学学报(哲学社会科学版),2006,27(2):187-190. |
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| 作者姓名： | 张建军 贾永录 肖辞元 |
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| 作者单位： | [1]西南石油大学计算机科学学院,四川成都610500 [2]西南石油大学工程学院,四川成都610500 |
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| 摘 要： | 根据常微分方程渐近解理论分别获得了二阶线性变系数齐次常微分方程在两组不同条件下的基本解组的渐近逼近式，证明了该方程在两组不同条件下所有解有界和零解全局渐近稳定．实例验证了本文所述方法的有效性．
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| 关 键 词： | 微分方程 全局渐近稳定 基本解组 渐近逼近式 |
| 文章编号： | 1673-5072（2006）02-0187-04 |
| 收稿时间： | 2006-01-10 |
| 修稿时间： | 2006年1月10日 |
Asymptotic Form of the Solution of a Class of Second Ordinary Differential Equations |
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| ZHANG Jian-jun, JIA Yong-lu, XIAO Ci-yuan.Asymptotic Form of the Solution of a Class of Second Ordinary Differential Equations[J].Journal of China West Normal University:Natural Science Edition,2006,27(2):187-190. |
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| Authors: | ZHANG Jian-jun JIA Yong-lu XIAO Ci-yuan |
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| Institution: | 1. College of Computer Science, Southwest Petroleum University, Chengdu 610500, China ; 2. College of Petroleum Engineering ,Soulhwest Petroleum University, Chengdu 610500, China |
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| Abstract: | This paper studies the asymptotic form of the basic solutions to the equation x..+a(t)x.+b(t)x=0 under the two different conditions and it proves the boundness of all solutions and the global asymptotic stability of the zero solution to the equation x..+a(t)x.+b(t)x=0.The examples show that the methods offered in this paper are efficient. |
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| Keywords: | differential equation global asymptotic stabilitv group for basic solutions asymptotic form of the solution |
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