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.
@article{bwmeta1.element.bwnjournal-article-cmv66i2p219bwm,
author = {Shyuichi Izumiya},
title = {Systems of Clairaut type},
journal = {Colloquium Mathematicae},
volume = {66},
year = {1993},
pages = {219-226},
zbl = {0821.35025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv66i2p219bwm}
}
Izumiya, Shyuichi. Systems of Clairaut type. Colloquium Mathematicae, Tome 66 (1993) pp. 219-226. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv66i2p219bwm/
[000] [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. | Zbl 0134.31004
[001] [2] A. C. Clairaut, Solution de plusieurs problèmes, Histoire de l'Académie Royale de Sciences, Paris, 1734, 196-215.
[002] [3] R. Courant and D. Hilbert, Methods of Mathematical Physics I, II, Wiley, New York, 1962. | Zbl 0099.29504
[003] [4] A. R. Forsyth, Theory of Differential Equations, Part III, Partial Differential Equations, Cambridge Univ. Press, London, 1906.
[004] [5] A. R. Forsyth, A Treatise on Differential Equations, Macmillan, London, 1885.
[005] [6] S. Izumiya, On Clairaut-type equations, Publ. Math. Debrecen, to appear. | Zbl 0822.34003
[006] [7] V. V. Lychagin, Local classification of non-linear first order partial differential equations, Russian Math. Surveys 30 (1975), 105-175.