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A Global Existence and Uniqueness Theorem for Ordinary Differential Equations

Published online by Cambridge University Press:  20 November 2018

W. Derrick  and
L. Janos
W. Derrick
Affiliation:
University of Montana
L. Janos
Affiliation:
University of Montana
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 1 , 01 March 1976 , pp. 105 - 107
Copyright
Copyright © Canadian Mathematical Society 1976

References

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