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ArticleOriginal scientific text

Title

Systems of Clairaut type

Authors 1

Affiliations

  1. Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060, Japan

Abstract

A characterization of systems of first order differential equations with (classical) complete solutions is given. Systems with (classical) complete solutions that consist of hyperplanes are also characterized.

Keywords

ENG
singular solutions, complete solutions, Clairaut equation

Bibliography

  1. C. Carathéodory, Calculus of Variations and Partial Differential Equations of First Order, Part I, Partial Differential Equations of the First Order, Holden-Day, San Francisco, 1965.
  2. A. C. Clairaut, Solution de plusieurs problèmes, Histoire de l'Académie Royale de Sciences, Paris, 1734, 196-215.
  3. R. Courant and D. Hilbert, Methods of Mathematical Physics I, II, Wiley, New York, 1962.
  4. A. R. Forsyth, Theory of Differential Equations, Part III, Partial Differential Equations, Cambridge Univ. Press, London, 1906.
  5. A. R. Forsyth, A Treatise on Differential Equations, Macmillan, London, 1885.
  6. S. Izumiya, On Clairaut-type equations, Publ. Math. Debrecen, to appear.
  7. V. V. Lychagin, Local classification of non-linear first order partial differential equations, Russian Math. Surveys 30 (1975), 105-175.
Colloquium Mathematicum
1993/66/2
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Pages:
219-226
Main language of publication
English
Received
1993-02-04
Published
1993
Exact and natural sciences