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Dichotomies and asymptotic behaviour for linear differential systems. (English) Zbl 0559.34049
General necessary and sufficient conditions that a system of differential equations (*) \(x'=A(t)x\) have a dichotomy are given in terms of Lyapunov type functions. Specific criteria are given which do not require either boundedness of the matrix A(t), or more generally that solutions of (*) have bounded growth or decay. A criterion using a generalized growth condition is also determined. Some further questions concerning the asymptotic behavior of solutions are addressed.
Reviewer: T.Gard

MSC:
34D05 Asymptotic properties of solutions to ordinary differential equations
34C30 Manifolds of solutions of ODE (MSC2000)
34A30 Linear ordinary differential equations and systems
34D20 Stability of solutions to ordinary differential equations
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