Advances in Differential Equations

Almost periodicity enforced by Coulomb friction

Klaus Deimling, Georg Hetzer, and Wen Xian Shen

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Adv. Differential Equations, Volume 1, Number 2 (1996), 265-281.

First available in Project Euclid: 25 April 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34C25: Periodic solutions
Secondary: 34A60: Differential inclusions [See also 49J21, 49K21] 70K20: Stability 70K30: Nonlinear resonances


Deimling, Klaus; Hetzer, Georg; Shen, Wen Xian. Almost periodicity enforced by Coulomb friction. Adv. Differential Equations 1 (1996), no. 2, 265--281.

Export citation