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April  1996, 2(2): 237-254. doi: 10.3934/dcds.1996.2.237

Existence and non-existence of homoclinic trajectories of the Liénard system

1. 

Department of Mathematics, Faculty of Science, Shinshu University, Matsumoto 390, Japan

2. 

Department of Mathematical Sciences, University of Osaka Prefecture, Sakai 593, Japan

Received  July 1995 Published  February 1996

In this paper we discuss the problem when the Liénard system $\dot{x}=y-F(x)$ and $\dot{y}=-g(x)$ has homoclinic trajectories or not. Some new criteria for the existence of periodic solutions of this system are also presented.
Citation: Jitsuro Sugie, Tadayuki Hara. Existence and non-existence of homoclinic trajectories of the Liénard system. Discrete and Continuous Dynamical Systems, 1996, 2 (2) : 237-254. doi: 10.3934/dcds.1996.2.237
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