Integral conditions on the asymptotic stability for the damped linear oscillator with small damping期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Integral conditions on the asymptotic stability for the damped linear oscillator with small damping

Authors:	L Hatvani

Institution:	Bolyai Institute, Aradi vértanúk tere 1, Szeged, Hungary, H--6720

Abstract:	The equation is considered under the assumption $0\le h(t)\le \overline{h}<\infty$ $(t\ge 0)$ . It is proved that $\limsup _{t \to \infty}\left(t^{-2/3}\int_0 ^t h\right)>0$ is sufficient for the asymptotic stability of , and is best possible here. This will be a consequence of a general result on the intermittent damping, which means that is controlled only on a sequence of non-overlapping intervals.

Keywords:	Intermittent damping energy method

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