Stability theory for ordinary differential equations.
Stability theory for ordinary differential equations.
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DOI：
10.1016/0022-0396(68)90048-x
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发表时间：
1968
影响因子：
2.4
通讯作者：
J. P. Lasalle
中科院分区：
文献类型：
--
作者：
J. P. Lasalle
The stability theory presented here was developed in a series of papers ([6]-[9]). The purpose of this paper is to refine the fundamental theorems and to provide proofs for results which previously had only been stated. The applications of this theory have been discussed and illustrated in the above-mentioned references and in [5]. For a discussion of and references to the exploitation of the “invariance principle” used here see [d] and [9]. For difference equations and applications to numerical analysis see [4]. In order to see how much is gained when it is known that the limit sets of solutions have an invariance property and for completeness we give first in Section 2 the best result we know for locating limit sets of nonautonomous systems. This result is an improvement of a theorem given by Yoshizawa in [IZ]. Section 3 is for autonomous ordinary differential equations, and from Theorems 2 and 3 follow all of the classical Liapunov results on the stability and instability of these systems.
