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On Disconjugate Differential Systems

Published online by Cambridge University Press:  20 November 2018

Philip Hartman
Affiliation:
The Johns Hopkins University
Aurel Wintner
Affiliation:
The Johns Hopkins University
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1. Introduction. Let F, G (and all capital letters to be used below) denote n by n matrices the elements of which are real-valued continuous functions on an interval a ≤t ≤ b. Correspondingly, by a solution x = x(t) of a differential system

1,

with det G(t) ≠ 0, or of a differential system

2,

will be meant a (vector) solution all n components of which are real-valued.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Lichtenstein, L., Article II C 12 (1924) in the Encyklopädie der Mathematischen Wissenschaften, 11.32.Google Scholar
2. Morse, M., A generalization of the Sturm separation and comparison theorems in n-space, Math. Ann. 103 (1930), 5269.Google Scholar
3. Ostrowski, A. M. and Taussky, O., On the variation of the determinant of a positive definite matrix, Koninkl. Nederl. Akad. Wetensch., Proceedings (A), 54 (1951), 383385.Google Scholar
4. Picard, E., Leçons sur quelques problèmes aux limites de la théorie des équations différentielles (Paris, 1930).Google Scholar
5. Poole, E. G. C., Introduction to the Theory of Linear Differential Equations (Oxford, 1936).Google Scholar
6. Wintner, A., On linear repulsive forces, Amer. J. Math., 71 (1949), 362366.Google Scholar
7. Wintner, A., On the non-existence of conjugate points, Amer. J. Math., 78 (1951), 368380.Google Scholar