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| 一类高阶微分方程组解的渐近行为 | |
| 引用本文： | 王青云,郝敦元,陆启韶.一类高阶微分方程组解的渐近行为[J].内蒙古大学学报(自然科学版),2005,36(6):601-607. |
| 作者姓名： | 王青云 郝敦元 陆启韶 |
| 作者单位： | 1. 北京航空航天大学理学院,北京,100083;内蒙古财经学院,呼和浩特,010051 2. 内蒙古大学理工学院,呼和浩特,010021 3. 北京航空航天大学理学院,北京,100083 |
| 基金项目： | 国家自然科学基金(10432010)资助~~ |
| 摘 要： | 对方程组Mx″ x′=f(t,x),x∈ΩRn,t∈R1,得到如下结果:若该方程组有一个解x1(t)满足limt→ ∞x1(t,t0,x11,x12)=c,则存在方程组x′=f(t,x)的一解x2(t)=x2(t,t0,x20),使得limt→ ∞‖x1(t,t0,x11,x12)-x2(t,t0,x20)‖=0.这一结果的某些推广和应用实例也在文中予以讨论. |
| 关 键 词： | 微分方程组 渐近行为 拓扑原理 |
| 文章编号： | 1000-1638(2005)06-0601-07 |
| 收稿时间： | 2004-09-28 |
| 修稿时间： | 2004年9月28日 |
Asymptotic Behavior of the Solutions of a Class of High Order Differential Equations |
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| WANG Qing-yun,HAO Dun-yuan,LU Qi-shao.Asymptotic Behavior of the Solutions of a Class of High Order Differential Equations[J].Acta Scientiarum Naturalium Universitatis Neimongol,2005,36(6):601-607. | |
| Authors: | WANG Qing-yun HAO Dun-yuan LU Qi-shao |
| Institution: | 1. School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, PRC; 2. Department of Mathematics, NeiMongol University, Hohhot 010021, PRC; 3. NeiMongol Finance and Economics College, Hohhot 010051, PRC |
| Abstract: | It is proved that for any solution x1(t) of the system Mx″+x′=f(t,x),in which limt→+∞x′1(t)=c,there exists a solution x2(t) of the system x′=f(t,x) such that limt→+∞‖x1(t;t0,x11,x12)-x2(t;t0,x2)‖=0.Furthermore, some generalizations of this result are also presented.Finally some examples are investigated explicitly. |
| Keywords: | differential equation asymptotic behavior topological principle |
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