| 一类四阶微分方程解的有界性和稳定性 |
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| 引用本文： | 俞元洪,陈文灯.一类四阶微分方程解的有界性和稳定性[J].应用数学和力学,1990,11(9):827-832. |
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| 作者姓名： | 俞元洪 陈文灯 |
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| 作者单位： | 1.中国科学院应用数学研究所; |
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| 摘 要： | 本文分两种情况研究方程(1):(i)P≡0,(ii)P(≠0)满足|P(t,x,y,z,ω)|≤(A+|y|+|z|+|ω|)q(t),这里,q(t)是t的非负函数.对于第一种情况研究了零解的全局渐近稳定性,对于第二种情况得到了方程(1)的有界性结果.这些结果改进并包含了一些已知的结果.
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| 关 键 词： | 微分方程 有界性 稳定性 |
| 收稿时间： | 1988-03-23 |
On the Boundedness and the Stability Properties of Solution of Certain Fourth Order Differential Equations |
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| Institution: | 1.Institute of Applied Mathematics, Academic Sinica, Beijing;2.Beijing Institute of Technology, Beijing |
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| Abstract: | This paper investigates equation(1)in two cases:(i)P≡0,(ii)P≠0 satisfies|P(i,x,y,z,w)<(A+|y|+|z|+|w|)q(t). where q(t) is a nonnegative function of t. For case(i)the asymptotic stability in the large of the trivial solution x=0 is investigated and for case(ii) the boundedness result is obtained for solutions of equation(1). These results improve and include several well-known results. |
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