Article Contents
Article Contents

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

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

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