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Non-resonance for linear differential systems

Published online by Cambridge University Press:  14 November 2011

M.S.P. Eastham  and
J.B. McLeod
M.S.P. Eastham
Affiliation:
King's College (University of London), Strand, London WC2R 2LS, U.K.
J.B. McLeod
Affiliation:
Mathematical Institute, St Giles, Oxford OX1 3LB, U.K.
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Synopsis

The existence of a set of real numbers σ, depending only on ∧0, is established such that if λ ∉ σ, the system Y'=(i∧0 + R)Y can be transformed into a system Z' = (i∧ + S)Z of the Levinson form. Here ∧0 and ∧ are real diagonal matrices, with ∧0 constant, and R(x) = ξ(x)T(λx). The scalar factor ξ(x) is o(l) (x →∞) and T belongs to a certain class of periodic matrices. The consequences for non-resonance, and the necessity of this class, are discussed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 1-2 , 1989 , pp. 103 - 122
Copyright
Copyright © Royal Society of Edinburgh 1989

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