Dichotomies and asymptotic behaviour for linear differential systems.

*(English)*Zbl 0559.34049General 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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\textit{J. S. Muldowney}, Trans. Am. Math. Soc. 283, 465--484 (1984; Zbl 0559.34049)

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##### References:

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