Geodesic
Exceptional Integrals of a not completely Integrable Total Differential Equation
Glasgow mathematical journal, Tome 1 (1953) no. 3, pp. 137-138

Voir la notice de l'article provenant de la source Cambridge University Press

1. There are exceptional integrals of the total differential equationin the case when it is not completely integrable, and so when the invariantis not identically zero, which do not seem to be mentioned by any standard authorities such as Cartan, Goursat, de la Vallée Poussin, and Schouten and Kulk. These are integrals of (1) which do not reduce I to zero. They arise only when the first partial derivates of P, Q, R are not all continuous. A simple example is z = 0 as an integral of 
Piaggio, H. T. H. Exceptional Integrals of a not completely Integrable Total Differential Equation. Glasgow mathematical journal, Tome 1 (1953) no. 3, pp. 137-138. doi: 10.1017/S2040618500035620
@article{10_1017_S2040618500035620,
     author = {Piaggio, H. T. H.},
     title = {Exceptional {Integrals} of a not completely {Integrable} {Total} {Differential} {Equation}},
     journal = {Glasgow mathematical journal},
     pages = {137--138},
     year = {1953},
     volume = {1},
     number = {3},
     doi = {10.1017/S2040618500035620},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500035620/}
}
TY  - JOUR
AU  - Piaggio, H. T. H.
TI  - Exceptional Integrals of a not completely Integrable Total Differential Equation
JO  - Glasgow mathematical journal
PY  - 1953
SP  - 137
EP  - 138
VL  - 1
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S2040618500035620/
DO  - 10.1017/S2040618500035620
ID  - 10_1017_S2040618500035620
ER  - 
%0 Journal Article
%A Piaggio, H. T. H.
%T Exceptional Integrals of a not completely Integrable Total Differential Equation
%J Glasgow mathematical journal
%D 1953
%P 137-138
%V 1
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S2040618500035620/
%R 10.1017/S2040618500035620
%F 10_1017_S2040618500035620

[(1)] (1)Cartan, E., Ann. Éc. Norm. Sup., (3), 16, 279, 280 (1899). Google Scholar

[(2)] (2)Goursat, E., Leçons sur le problème de Pfqff (Paris, 1922), pp. 187–190. Google Scholar

[(3)] (3)de la Vallée Poussin, Ch.-J., Cours d'Analyse Infinitésimale, t. II. (7th ed., 1946), pp. 303–4. Google Scholar

[(4)] (4)Sohouten, J. A., and Kulk, W. V. D., Pfqff's Problem and its Generalizations (Oxford, 1949). Google Scholar

Cité par Sources :