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On the Forced Lienard Equation

Published online by Cambridge University Press:  20 November 2018

R.R. Stevens
R.R. Stevens*
Affiliation:
University of Montana
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We consider the second order differential equation

(1)

with the assumptions that

(2) f(x) is continuous (- ∞ < x < ∞) and p(t) is continuous and bounded: |p(t)| ≤ E, - ∞ < t < ∞.

Also, throughout this paper, F(x) denotes an antiderivative of f(x).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 1 , February 1969 , pp. 79 - 84
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. de la Vallée Poussin, C.J., Leçons sur l'approximation des Fonctions d'une Variable Réele. (Gauthiers-Villars, Paris, 1919).Google Scholar
2. Frederickson, P. and Lazer, P. A., Necessary and sufficient amplitude dependent damping for a bounded solution. (To appear).Google Scholar
3. Sansone, G. and Conti, R., Non-linear differential equations. (New York, 1964).Google Scholar
4. Loud, W. S., Behaviour of certain forced nonlinear systems of second order under large forcing. Duke Math. J. 24 (1957) 235–247.Google Scholar