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首页> 外文期刊>Journal of dynamics and differential equations >The Bohl Spectrum for Linear Nonautonomous Differential Equations
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The Bohl Spectrum for Linear Nonautonomous Differential Equations

机译：线性非自治微分方程的Bohl谱

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摘要

We develop the Bohl spectrum for nonautonomous linear differential equations on a half line, which is a spectral concept that lies between the Lyapunov and the Sacker-Sell spectra. We prove that the Bohl spectrum is given by the union of finitely many intervals, and we show by means of an explicit example that the Bohl spectrum does not coincide with the Sacker-Sell spectrum in general even for bounded systems. We demonstrate for this example that any higher-order nonlinear perturbation is exponentially stable (which is not evident from the Sacker-Sell spectrum), but we show that in general this is not true. We also analyze in detail situations in which the Bohl spectrum is identical to the Sacker-Sell spectrum.
机译：我们在半线上开发了非自治线性微分方程的Bohl谱，这是一个位于Lyapunov和Sacker-Sell谱之间的谱概念。我们证明了Bohl谱是由有限多个间隔的并集给出的，并且我们通过一个明确的例子表明，即使对于有界系统，Bohl谱也通常与Sacker-Sell谱不重合。在这个例子中，我们证明了任何高阶非线性扰动都是指数稳定的（这在Sacker-Sell频谱中并不明显），但是我们证明总体上是不正确的。我们还详细分析了Bohl谱与Sacker-Sell谱相同的情况。

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