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Instability theorems for certain nth order differential equations

Part of: Stability theory

Published online by Cambridge University Press:  09 April 2009

Li Wen-Jian  and
Duan Kui-chen
Li Wen-Jian
Affiliation:
Xinjiang Bayi Agricultural College, Urumqi, China
Duan Kui-chen
Affiliation:
Xinjiang University, Urumqi, China
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Abstract

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In this paper we study the instability of certain nth order differential equations by means of Liapunov's functions and obtain some sufficient conditions for the equations being unstable. A method of constructing Liapunov's function for instability is being perfected. In particular the problem Ezeio posed in 1982 has been resolved to some extent.

Keywords

high order differential equationinstabilityLiapunov's function.

MSC classification

Secondary: 34D20: Stability
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 1 , August 1995 , pp. 1 - 7
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Ezeilo, J. O. C., ‘Instability theorems for a certain fifth-order differential equations’, Math. Proc. Cambridge Philos. Soc. 84 (1978), 343–350.CrossRefGoogle Scholar
[2]Ezeilo, J. O. C., ‘An instability theorem for a certain sixth order differential equation’, J. Austral. Math. Soc. (Ser. A) 32 (1982), 129–133.CrossRefGoogle Scholar
[3]Reissig, R., Sansone, G. and Conti, R., Nonlinear differential equations of high order (Noordhoff, Groningen, 1974).Google Scholar
[4]Wen-jian, Li and Yuan-hong, Yu, ‘Instability theorems for some fourth and fifth order differential equations’, J. Xinjiang Univ. Nat. Sci. 7 (1990), 8–12.Google Scholar
[5]Zhen-hai, Zhao, ‘Implementation of the routh criterion on electronic computers’, J. Dalian Inst. Tech. 27 (1988), 127–130.Google Scholar