scholarly journals Periodic Solutions of a Certain Generalized Liénard Equation

2004 ◽  
Vol 47 (1) ◽  
pp. 41-61 ◽  
Author(s):  
Duccio Papini ◽  
Gabriele Villari
Keyword(s):  
Periodic Solutions ◽  
Liénard Equation ◽  
Generalized Liénard Equation ◽  
Lienard Equation

On the Liénard system which has no periodic solutions

1993 ◽  
Vol 113 (2) ◽  
pp. 413-422 ◽  
Author(s):  
Jitsuro Sugie ◽  
Toshiaki Yoneyama
Keyword(s):  
Periodic Solutions ◽  
Limit Cycles ◽  
Sufficient Conditions ◽  
Liénard Equation ◽  
Liénard System ◽  
Lienard System ◽  
Generalized Liénard Equation ◽  
Existence Of Periodic Solutions ◽  
Image Position ◽  
Lienard Equation

The problem of periodicity of solutions of the generalized Liénard equationhas attracted much attention. Many efforts have been made to give sufficient conditions to guarantee the existence and the uniqueness of periodic solutions (limit cycles) of (1·1). There are also some papers on the number of limit cycles of (1·1) (see, for example, [3, 5, 6, 13]). However, there are only a few results on non-existence of periodic solutions of (1·1).

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