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Asymptotic formulae for linear oscillations

Published online by Cambridge University Press:  18 May 2009

F. V. Atkinson
F. V. Atkinson
Affiliation:
The Canberra University College, Canberra, Australian Capital Territory, Australia
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A number of formulae are known which exhibit the asymptotic behaviour as t→∞ of the solutions of

The aim of thisnote is to unify a group of such formulae, relating to the case in which F(t) iS on the whole positive, and suitably continuous though not necessarily analytic.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 3 , Issue 3 , December 1957 , pp. 105 - 111
Copyright
Copyright © Glasgow Mathematical Journal Trust 1957

References

REFERENCES

1.Ascoli, G., Revista Univ. Nac. de Tucumdn, Serie A: Mat. y Fis. Tedr, 2 (1941), 131–140.Google Scholar
2.Ascoli, G., Annali di Mat. Pur. Appl., (4) 26(1947), 199–206.Google Scholar
3.Levinson, N., Duke Math. J., 15 (1948), 111–126.CrossRefGoogle Scholar
4.Atkinson, F. V., Annali di Mat. Pur. Appl., (4) 37 (1954), 347–378.CrossRefGoogle Scholar
5.Wintner, A., Phys. Rev., 72 (1947), 516–517.CrossRefGoogle Scholar
6.Atkinson, F. V., Univ. Nac. del Tucumdn, Revista, Serie A, Mat. y Fis. Tedr., 8 (1951), 71–87.Google Scholar
7.Hartman, P. and Wintner, A., Ainer. J. Math., 77 (1955), 45–86.CrossRefGoogle Scholar
8.Bellman, R., Stability theory of differential equations(New York, 1953).Google Scholar
9.Bellman, R., Duke Math. J., 22 (1955), 511–513.CrossRefGoogle Scholar
10.Gusarov, L. A., Moskov. Gos. Univ. Uc. Zap., 165, Mat. 7 (1954), 223–237.Google Scholar
11.Sobol, I. M., Mat. Sbornik (N.S) 28 (70) (1951), 707–714.Google Scholar