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Analytical theory of non-linear oscillations

I. An existence theorem for periodic oscillations of equations of the second order

Published online by Cambridge University Press:  24 October 2008

Chike Obi
Chike Obi
Affiliation:
Mathematics Department, University of Lagos, Nigeria
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Extract

In this paper, we improve on the results of two previous papers (8, 9) by establishing a general existence theorem (section 1·3, below) for a class of periodic oscillations of a wide class of non-linear differential equations of the second order in the real domain which are perturbations of the autonomous differential equation

where g(x) is strictly non-linear. We then, by way of illustrating the power of the theorem, apply it to the problems which Morris (section 2·2 below), Shimuzu (section 2·3 below) and Loud (section 2·5 below) set themselves on the existence of periodic oscillations of certain differential equations which are perturbations of equations of the form (1·1·1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 285 - 296
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

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