Geodesic
A Global Existence and Uniqueness Theorem for Ordinary Differential Equations
Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 105-107

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

As observed by A. Bielecki and others ([1], [3]) the Banach contraction principle, when applied to the theory of differential equations, provides proofs of existence and uniqueness of solutions only in a local sense. S. C. Chu and J. B. Diaz ([2]) have found that the contraction principle can be applied to operator or functional equations and even partial differential equations if the metric of the underlying function space is suitably changed. 
Derrick, W.; Janos, L. A Global Existence and Uniqueness Theorem for Ordinary Differential Equations. Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 105-107. doi: 10.4153/CMB-1976-015-7
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[1] 1. Bielicki, A., Une remarque sur le méthode de Banach-Cacciopoli-Tikhonov dans la théorie des equations différentielles ordinaires, Bull. Acad. Polon. Sci. 4, 1956, pp. 261–264. Google Scholar

[2] 2. Chu, S. C. and Diaz, J. B., A Fixed point theorem for “in large” applications of the contraction principle, A. D. Ac. di Torino, Vol. 99 (1964–65), pp. 351–363. Google Scholar

[3] 3. Janos, L., Contraction property of the operator of integration, Can. Math. Bull/ (to appear). Google Scholar

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