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Solutions of a non-linear differential equation. II

Published online by Cambridge University Press:  24 October 2008

C. E. Billigheimer
C. E. Billigheimer
Affiliation:
University of Toronto
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Extract

We consider in this paper the solution behaviour as s → 0 of the equation

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

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 1 , January 1968 , pp. 127 - 139
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Bellman, R.Stability theory of differential equations (McGraw-Hill; New York, 1953).Google Scholar
(2)Bieberbach, L.Theorie der differentialgleichungen, vol. VI. Grundlehren der Mathematischen Wissenschaften (Springer; Berlin, 1923).CrossRefGoogle Scholar
(3)Billiigheimer, C. E.Solutions of a nonlinear partial differential equation of hyperbolic type. Quart. Appl. Math. 25 (1967), 19–30.CrossRefGoogle Scholar
(4)Billigheimer, C. E.Solutions of a non-linear differential equation. I. Proc. Cambridge Philos. Soc. 63 (1967), 734–754.CrossRefGoogle Scholar
(5)Fowler, R. K.The solutions of Emden's and similar differential equations. Monthly Notices Roy. Astronom. Soc. 91 (1930–1931), 63–91.CrossRefGoogle Scholar
(6)Fowler, R. K.Further studies of Emden's and similar differential equations. Quart. J. Math. Oxford Ser. (1931), 259–288.CrossRefGoogle Scholar
(7)Goursat, E. Differential equations, Cours d'Analyse II, (2) (Transl.) (Ginn and Co.; Boston, 1917).Google Scholar
(8)Jeffreys, K. and Jeffreys, B. S.Methods of mathematical physics (Cambridge University Press; Cambridge, 1956).Google Scholar
(9)Mitskevich, N. V.The scalar field of a stationary nucleon in a nonlinear theory. J. exp. theor. Phys. II. 2 (1956), 197–202.Google Scholar
(10)Finkelstein, R., Le Levier, R. and Ruderman, M.Nonlinear spinor fields. Phys. Rev. 83 (1951), 326–332.CrossRefGoogle Scholar