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

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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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     title = {A {Global} {Existence} and {Uniqueness} {Theorem} for {Ordinary} {Differential} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {105--107},
     year = {1976},
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     doi = {10.4153/CMB-1976-015-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-015-7/}
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