Systems of Clairaut type

• Autorzy: Shyuichi Izumiya
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

singular solutions; complete solutions; Clairaut equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 66
• Numer: 2
• Strony: 219-226

Daty

wydano

1993

otrzymano

1993-02-04

Twórcy

autor

Shyuichi Izumiya

• Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060, Japan

Bibliografia

• [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.