On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities

Jaume Llibre, Enrique Ponce, Francisco Torres

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Resum

In this paper we study the non-existence and the uniqueness of limit cycles for the Liénard differential equation of the form x″ - f(x)x′ + g(x) = 0 where the functions f and g satisfy xf(x) > 0 and xg(x) > 0 for x ≠ 0 but can be discontinuous at x = 0. In particular, our results allow us to prove the non-existence of limit cycles under suitable assumptions, and also prove the existence and uniqueness of a limit cycle in a class of discontinuous Liénard systems which are relevant in engineering applications. © 2008 IOP Publishing Ltd and London Mathematical Society.
Idioma originalEnglish
Pàgines (de-a)2121-2142
RevistaNonlinearity
Volum21
DOIs
Estat de la publicacióPublicada - 1 de set. 2008

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