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

 

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Opened Access On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities
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Author: Llibre Saló, Jaume
Ponce Núñez, Enrique
Torres Peral, Francisco
Department: Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
Date: 2008
Published in: Nonlinearity, 21 (9), 2121-2142.
Document type: Article
Abstract: 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.
Cite: Llibre Saló, J., Ponce Núñez, E. y Torres Peral, F. (2008). On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities. Nonlinearity, 21 (9), 2121-2142.
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URI: http://hdl.handle.net/11441/58704

DOI: 10.1088/0951-7715/21/9/013

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