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Further results for the solutions of a third-order differential equation

Published online by Cambridge University Press:  24 October 2008

J. O. C. Ezeilo
J. O. C. Ezeilo
Affiliation:
Department of Mathematics, University College, Ibadan, Nigeria
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Extract

1. The equation considered here is of the form

where a, b are constants, h(x) is differentiable and h′(x), p(t) are continuous in x, t respectively. The primary object of the paper is to prove the following

Theorem 1. Suppose that

(i) a > 0,b > 0;

(ii) h(0) = 0, h(x)/x ≥ δ > 0 (x ≠ 0);

(iii) h′(x) ≤ c for all x where ab > c > 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 1 , January 1963 , pp. 111 - 116
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Barbasin, E. A.On the stability of the solution of a certain non-linear equation of the third order. Prikl. Mat. Meh. 16 (1952) 629–632 (in Russian; translation available from D.S.I.R.).Google Scholar
(2)Ezeilo, J. O. C.On the stability of solutions of certain differential equations of the third order. Quart. J. Math. Oxford Ser. (2) 11 (1960), 64–69.CrossRefGoogle Scholar
(3)Ezeilo, J. O. C.An elementary proof of a boundedness theorem for a certain third order differential equation. J. London Math. Soc. (to appear).Google Scholar
(4)Lefschetz, S.Differential equations: geometric theory. (Interscience: New York, 1957).Google Scholar