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Remarks on the asymptotic behaviour of perturbed linear systems†

Published online by Cambridge University Press:  18 May 2009

James S. W. Wong
James S. W. Wong
Affiliation:
University of AlbertaEdmonton, AlbertaCanada Carnegie Mellon UniversityPittsburgh, PennsylvaniaU.S.A..
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We are here concerned with following result of Trench:

Theorem. (Trench [5]). Let v1 and v2 be two linearly independent solutions of the differential equation

where a(t) is continuous on [0, ∞), and let b(t) be a continuous function of t for t ≧ 0 satisfying

where m(t) = max {|v1(t)|2, |v2(t)|2}. Then, if α1and α2are two arbitrary constants, there exists a solution u of

which can be written in the form

,

with

fori = 1, 2.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 10 , Issue 2 , July 1969 , pp. 116 - 120
Copyright
Copyright © Glasgow Mathematical Journal Trust 1969

References

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