Kodai Mathematical Journal

How to define singular solutions

Shyūichi Izumiya and Jian Ming Yu

Full-text: Open access

Article information

Source
Kodai Math. J. Volume 16, Number 2 (1993), 227-234.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1138039786

Digital Object Identifier
doi:10.2996/kmj/1138039786

Mathematical Reviews number (MathSciNet)
MR1225531

Zentralblatt MATH identifier
0794.34003

Subjects
Primary: 34A09: Implicit equations, differential-algebraic equations [See also 65L80]
Secondary: 34A26: Geometric methods in differential equations 34A34: Nonlinear equations and systems, general

Citation

Izumiya, Shyūichi; Yu, Jian Ming. How to define singular solutions. Kodai Math. J. 16 (1993), no. 2, 227--234. doi:10.2996/kmj/1138039786. https://projecteuclid.org/euclid.kmj/1138039786.


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References

  • [1] V. I. ARNOL'D, Contact geometry and wave propagation, Monographic de Ln-seignement Mathematique 34 (1989).
  • [2] C. CARATHEODORY, Calculus of Variations and Partial Differential Equations o First Order, Part I, Partial Differential Equations of the First Order, Holden-Day, 1965.
  • [3] R. COURANT AND D. HILBERT, Methods of mathematical physics I, II, Wiley, New York, 1962
  • [4] A. R. FORSYTH, A Treatise on differential equations, Macmillan and Co, 1885
  • [5] A. R. FORSYTH, Theory of differentialequations, Part III partialdifferentia equations. Cambridge Univ. Press, London, 1906.
  • [6] M. FUKUDA AND T. FUKUDA, Singular solutions of ordinary differential equa tions, The Yokohama Math. Jour. 15 (1977), 41-58.
  • [7] E. L. INCE, Ordinary differential equations, Dover, 1926
  • [8] S. IZUMIYA, Singular solutions of first order differential equations, to appear i Bull. London Math. Soc.
  • [9] I. G. PETROVSKI, Ordinary differential equations, Prentice-Hall, 1996
  • [10] J. Yu, On singular solutions of completely integrable partial differential equa tions of first order, in preparation.