Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T14:26:04.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniformly almost periodic solutions of non-linear differential equations of the second order I. General exposition†

Published online by Cambridge University Press:  24 October 2008

Chike Obi
Chike Obi
Affiliation:
University College Ibadan Nigeria, West Africa
Get access Rights & Permissions [Opens in a new window]

Extract

1·1. A general problem in the theory of non-linear differential equations of the second order is: Given a non-linear differential equation of the second order uniformly almost periodic (u.a.p.) in the independent variable and with certain disposable constants (parameters), to find: (i) the non-trivial relations between these parameters such that the given differential equation has a non-periodic u.a.p. solution; (ii) the number of periodic and non-periodic u.a.p. solutions which correspond to each such relation; and (iii) explicit analytical expressions for the u.a.p. solutions when they exist.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 4 , October 1955 , pp. 604 - 613
Copyright
Copyright © Cambridge Philosophical Society 1955

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Brown, E. C.Amer. J. Math. 60 (1938), 785, §9.CrossRefGoogle Scholar
(2)Moulton, F. R.Differential equations (New York, 1930).Google Scholar
(3)Obi, Chike. J. Lond. math. Soc. 25 (1950), 217–26.CrossRefGoogle Scholar
(4)Obi, Chike. Proc. Camb. phil. Soc. 47 (1951), 741–51.CrossRefGoogle Scholar
(5)Van Der Pol, B.Proc. Inst. Radio Engrs, N.Y., 22 (1934), 1080–2.Google Scholar
(6)Reuter, G. E. H.J. Lond. math. Soc. 26 (1951).Google Scholar
(7)Stoker, J. J.Non-linear vibrations (New York, 1950).Google Scholar