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1996 Almost periodicity enforced by Coulomb friction
Klaus Deimling, Georg Hetzer, Wen Xian Shen
Adv. Differential Equations 1(2): 265-281 (1996).


We describe the influence of Coulomb friction $\mu$ sgn $ \dot x$ on the behavior of the linear oscillator given by $\ddot x+x=\varphi(t)$, where $\varphi$ is continuous and almost periodic. Depending on $\varphi$, we characterize the range of $\mu>0$ such that nontrivial almost periodic motions exist. We also show that dissipation caused by Coulomb friction may be too weak to ensure uniqueness of such motions, a phenomenon which appears already in case $\varphi$ is $2k\pi$-periodic with $k>1$. Nevertheless, we get a rather complete picture of the asymptotic behavior of such a system, but also have some interesting open questions, for example concerning the shape of the almost periodic solutions.


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Klaus Deimling. Georg Hetzer. Wen Xian Shen. "Almost periodicity enforced by Coulomb friction." Adv. Differential Equations 1 (2) 265 - 281, 1996.


Published: 1996
First available in Project Euclid: 25 April 2013

zbMATH: 0838.34016
MathSciNet: MR1364004

Primary: 34C25
Secondary: 34A60 , 70K20 , 70K30

Rights: Copyright © 1996 Khayyam Publishing, Inc.


Vol.1 • No. 2 • 1996
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