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Solutions of a non-linear differential equation. I

Published online by Cambridge University Press:  24 October 2008

C. E. Billigheimer
Affiliation:
Department of Mathematics, University of Toronto

Extract

We consider in this paper solutions of the equation

where the primes indicate differentiation with respect to s, and a, b, c are constants.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Ascoli, G.Ricerche asintotiche sopra una classe di equazioni differenziali non lineari. Ann. Scuola Norm. Sup. Pisa (3), 5 (1951), 128.Google Scholar
(2)Atkinson, F. V.On asymptotically linear second-order oscillations. On asymptotically linear second-order oscillations 4, 5 (1955), 789793.Google Scholar
(3)Bellman, R.Stability theory of differential equations (McGraw Hill; New York, 1953).Google Scholar
(4)Bieberbach, L.Theorie der Differentialgleichungen, vol. vi. Grundlehren der Mathematischen Wissenschaften (Springer; Berlin, 1923).CrossRefGoogle Scholar
(5)Billigheimer, C. E.Solutions of a nonlinear partial differential equation of hyperbolic type. Quart. Appl. Math. 25 (1967), 1930.CrossRefGoogle Scholar
(6)Billigheimer, C. E. Asymptotically linear second-order differential equations. (To be published.)Google Scholar
(7)Fowler, R. H.The solutions of Emden's and similar differential equations. Monthly Not. Roy. Astr. Soc. 91 (19301931), 6391.CrossRefGoogle Scholar
(8)Fowler, R. H.Further studies of Emden's and similar differential equations of first order. Proc. London Math. Soc. (2), 32 (1931), 259288.Google Scholar
(9)Goursat, E.Differential equations, cours d'analyse II, (2) (Transl.) (Ginn and Co.; Boston, 1917).Google Scholar
(10)Hardy, G. H.Real continuous solutions of algebraic differential equations of first order. Proc. London Math. Soc. (2), 10 (1912), 451–68.CrossRefGoogle Scholar
(11)Levinson, N.The asymptotic behaviour of a system of linear differential equations. Amer. J. Math. 68 (1946), 16.CrossRefGoogle Scholar
(12)Weyl, H.Comment on the preceding paper. Amer. J. Math. 68 (1946), 712.CrossRefGoogle Scholar