DocumentCode :
1167010
Title :
Existence and uniqueness results for Lienard´s equations
Author :
de Figueiredo, Rui J.P.
Volume :
17
Issue :
3
fYear :
1970
fDate :
8/1/1970 12:00:00 AM
Firstpage :
313
Lastpage :
321
Abstract :
A new set of conditions for the existence and uniqueness of the periodic solution of the equation 
(superscript dot = 
) is given. Lyapunov-like functions are used in the derivation of the results. This permits the formulation of the existence and uniqueness conditions in a simple yet general way. The present conditions include those of Libnard and Levinson and Smith when particularized to the above equation. They also permit the inclusion of most of the cases of two-stroke oscillators covered by the author\´s previous theorems for equations of the above type. Periodicity results for the forced equation 
with 
periodic and bounded are also given.
(superscript dot = ) is given. Lyapunov-like functions are used in the derivation of the results. This permits the formulation of the existence and uniqueness conditions in a simple yet general way. The present conditions include those of Libnard and Levinson and Smith when particularized to the above equation. They also permit the inclusion of most of the cases of two-stroke oscillators covered by the author\´s previous theorems for equations of the above type. Periodicity results for the forced equation with periodic and bounded are also given.Keywords :
Circuit theory; Automatic control; Error analysis; Feedback control; Finite wordlength effects; Laplace equations; Linear approximation; Linear systems; Nonlinear equations; Oscillators; Transient response;
fLanguage :
English
Journal_Title :
Circuit Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9324
Type :
jour
DOI :
10.1109/TCT.1970.1083127
Filename :
1083127
Link To Document :
