A Necessary and Sufficient Condition for the Oscillation of Solutions of Lienard Type System with Multiple Singular Points

Sun Jitao; Zhang Yinping

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Article Navigation > Applied Mathematics and Mechanics > 1997 > 18(12): 1125-1129

Sun Jitao, Zhang Yinping. A Necessary and Sufficient Condition for the Oscillation of Solutions of Lienard Type System with Multiple Singular Points[J]. Applied Mathematics and Mechanics, 1997, 18(12): 1125-1129.

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A Necessary and Sufficient Condition for the Oscillation of Solutions of Lienard Type System with Multiple Singular Points

Shanghai Tiedao University, Shanghai 200333, P. R. China

Received Date: 1995-09-06
Rev Recd Date: 1997-03-26
Publish Date: 1997-12-15

Abstract

Abstract

In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also extended and improved in this paper.
- Liénard type system,
- oscillating solution,
- necessary and sufficient condition

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References(12)

References

[1]	J.R.Graef.On the Generalized Liénard equation with negative damping.J.Diff.Eqs12 (1972),34~62.
[2]	G.Villari,On the qualitative behaviour of solutions of Liénard equation.J.Diff Eqs.67 (1987),269-27.
[3]	韩茂安,关于方程的周期解:无界解及振荡解南京大学学报数学半年刊.1 (1984),89-101.
[4]	孙继涛,系统的解振动的充要条件,南京大学学报数学半年刊,9(1992),113-119.
[5]	李继彬,平面三次系统的一类极限环分布,中国科学(A辑) (7) (1984),586-596.
[6]	A.Sandquist and K.M.Andersen,A necessary and sufficient condition for the existenceof unique nontrivial periodic solution to a class of equations of Lienard type,J.Diff Eqs.46 (1982).356-378.
[7]	王现,关于Liénard型系统之极限环的注,数学季刊,5(1990),122-130.
[8]	孙继涛,Liénard型系统解的有界性及极限环的存在性高校应用数学学报,7 (1992),184-191.
[9]	韩茂安,具有多个奇点的微分方程的全局性质数学学报,33 (1990),684-693.
[10]	孙继涛,Liénard型系统的定性行为,数学物理学报,14 (1994),90-95.
[11]	T Hara and T.Yoneyama,On the global center of generalized Lienard equation and itsapplication to stability problems,Funkical.Ekrac.28 (1985),171-192.
[12]	G.Villari and F.Zanolin,On a dynamical system in the Lienard plane.necessary andsufficient conditions for the intersection with the vertical isocline and applications,FI,nkical.Ekvac.33 (1990),19-38.