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

Jitsuro Sugie; Tadayuki Hara

doi:10.3934/dcds.1996.2.237

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1996, Volume 2, Issue 2: 237-254. Doi: 10.3934/dcds.1996.2.237

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

Jitsuro Sugie¹ and
Tadayuki Hara²

1.
Department of Mathematics, Faculty of Science, Shinshu University, Matsumoto 390
2.
Department of Mathematical Sciences, University of Osaka Prefecture, Sakai 593

Received: July 1995

Published: April 1996

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Abstract

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.

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Mathematics Subject Classification: Primary: 34C05, 34C25, 34C37; Secondary: 70K05, 70K10.

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