Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-27T19:39:00.307Z Has data issue: false hasContentIssue false

Asymptotic formulae for linear oscillations

Published online by Cambridge University Press:  18 May 2009

F. V. Atkinson
Affiliation:
The Canberra University College, Canberra, Australian Capital Territory, Australia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
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), 131140.Google Scholar
2.Ascoli, G., Annali di Mat. Pur. Appl., (4) 26(1947), 199206.Google Scholar
3.Levinson, N., Duke Math. J., 15 (1948), 111126.CrossRefGoogle Scholar
4.Atkinson, F. V., Annali di Mat. Pur. Appl., (4) 37 (1954), 347378.CrossRefGoogle Scholar
5.Wintner, A., Phys. Rev., 72 (1947), 516517.CrossRefGoogle Scholar
6.Atkinson, F. V., Univ. Nac. del Tucumdn, Revista, Serie A, Mat. y Fis. Tedr., 8 (1951), 7187.Google Scholar
7.Hartman, P. and Wintner, A., Ainer. J. Math., 77 (1955), 4586.CrossRefGoogle Scholar
8.Bellman, R., Stability theory of differential equations(New York, 1953).Google Scholar
9.Bellman, R., Duke Math. J., 22 (1955), 511513.CrossRefGoogle Scholar
10.Gusarov, L. A., Moskov. Gos. Univ. Uc. Zap., 165, Mat. 7 (1954), 223237.Google Scholar
11.Sobol, I. M., Mat. Sbornik (N.S) 28 (70) (1951), 707714.Google Scholar