Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the asymptotic stability of oscillators with unbounded damping

Authors: Zvi Artstein and E. F. Infante
Journal: Quart. Appl. Math. 34 (1976), 195-199
MSC: Primary 34D05
DOI: https://doi.org/10.1090/qam/466789
MathSciNet review: 466789
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Abstract: Through a technique inspired by the invariance principle of LaSalle, a general growth condition on the damping coefficient $ h\left( t \right)$ of the equation

$\displaystyle \ddot x + h\left( t \right)\dot x + kx = 0, k > 0,h(t) \ge \epsilon > 0$

, is given which is sufficient for the global asymptotic stability of the origin yet permits this coefficient to grow to infinity with time. The methods used do not depend on linearity, and are applied to obtain similar results to the nonlinear analogue of this equation.

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DOI: https://doi.org/10.1090/qam/466789
Article copyright: © Copyright 1976 American Mathematical Society

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