# Systems of Clairaut type

Colloquium Mathematicae (1993)

- Volume: 66, Issue: 2, page 219-226
- ISSN: 0010-1354

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top## How to cite

topIzumiya, Shyuichi. "Systems of Clairaut type." Colloquium Mathematicae 66.2 (1993): 219-226. <http://eudml.org/doc/210244>.

@article{Izumiya1993,

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.},

author = {Izumiya, Shyuichi},

journal = {Colloquium Mathematicae},

keywords = {singular solutions; complete solutions; Clairaut equation; equations of Clairaut type},

language = {eng},

number = {2},

pages = {219-226},

title = {Systems of Clairaut type},

url = {http://eudml.org/doc/210244},

volume = {66},

year = {1993},

}

TY - JOUR

AU - Izumiya, Shyuichi

TI - Systems of Clairaut type

JO - Colloquium Mathematicae

PY - 1993

VL - 66

IS - 2

SP - 219

EP - 226

AB - 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.

LA - eng

KW - singular solutions; complete solutions; Clairaut equation; equations of Clairaut type

UR - http://eudml.org/doc/210244

ER -

## References

top- [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. Zbl0134.31004
- [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. Zbl0099.29504
- [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. Zbl0822.34003
- [7] V. V. Lychagin, Local classification of non-linear first order partial differential equations, Russian Math. Surveys 30 (1975), 105-175.

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