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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Dichotomies and asymptotic behaviour for linear differential systems

Author: James S. Muldowney
Journal: Trans. Amer. Math. Soc. 283 (1984), 465-484
MSC: Primary 34D99
MathSciNet review: 737880
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Abstract: Sufficient conditions that a system of differential equations $ x' = A(t)x$ have a dichotomy usually require that the matrix $ A(t)$ be bounded or at least that some restriction be placed on the rate of growth or decay of solutions. Here three sets of necessary and sufficient conditions for a dichotomy which do not impose such a restriction are given in terms of Liapunov functions. Each of the theorems gives practical criteria for a dichotomy including the extension to unbounded matrices of criteria which depend on a concept of diagonal dominance for $ A(t)$. An asymptotic analysis is also given for subspaces of the solution set by means of the associated compound equations.

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Article copyright: © Copyright 1984 American Mathematical Society