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Asymptotic formulae for linear equations

Published online by Cambridge University Press:  18 May 2009

Don B. Hinton
Don B. Hinton
Affiliation:
University of Tennessee, Knoxville, Tennessee
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Numerous formulae have been given which exhibit the asymptotic behaviour as t → ∞solutions of

where F(t) is essentially positive and Several of these results have been unified by a theorem of F. V. Atkinson [1]. It is the purpose of this paper to establish results, analogous to the theorem of Atkinson, for the third order equation

and for the fourth order equation

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 2 , September 1972 , pp. 147 - 152
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

1.Atkinson, F. V., Asymptotic formulae for linear oscillations, Proc. Glasgow Math. Assoc. 3 (1957), 105–111.Google Scholar
2.Birkhoff, G. and MacLane, S., A Survey of Modern Algebra, 2nd edition (New York, 1953).Google Scholar
3.Coddington, E. A. and Levinson, N., Theory of Ordinary Differential Equations (New York, 1955).Google Scholar
4.Hinton, D. B., Asymptotic behaviour of solutions of (ry(m))(k) ±qy = 0, J. Differential Equations 4 (1968), 590–596.Google Scholar