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An infinite class of periodic solutions of ẍ + 2x3 = p(t)

Published online by Cambridge University Press:  24 October 2008

G. R Morris
G. R Morris
Affiliation:
University of Queensland, Brisbane
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Extract

An important unsolved problem in the theory of non-linear oscillations is to establish the boundedness or unboundedness of the general solution of

where dots denote differentiation with respect to t. When p(t) is periodic, we may seek periodic solutions. This search is interesting for its own sake, and of course leads us to special bounded solutions. In three previous papers (2, 3, 4) I have exhibited the equation

as tractable: on the assumption that e(t) is even and periodic, it was shown that the equation has an infinity of periodic solutions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 157 - 164
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

REFERENCES

(1)Levinson, N.Transformation theory of non-linear differential equations of the second order. Ann. of Math. (2) 45 (1944), 723–737.CrossRefGoogle Scholar
(2)Morris, G. R.A differential equation for undamped forced non-linear oscillations. I. Proc. Cambridge Philos. Soc. 51 (1955), 297–312.CrossRefGoogle Scholar
(3)Morris, G. R.A differential equation for undamped forced non-linear oscillations. II. Proc. Cambridge Philos. Soc. 54 (1958), 426–438.CrossRefGoogle Scholar
(4)Morris, G. R.A differential equation for undamped forced non-linear oscillations. III. Proc. Cambridge Philos. Soc. 61 (1965), 133–155.CrossRefGoogle Scholar