On the existence of quasi-periodic lattice oscillations

Stability of non-sticking periodic oscillations obtained via the averaging method in discontinuous systems. I. Smooth outside of the discontinuity surfaces systems

In this paper the statement of the second Bogolyubov's theorem on periodic solutions of smooth systems with small parameter is justified for discountinuous systems. It is assumed that the generating solution intersects the discontinuity hyperplanes transversally and that the system is smooth outside of these hyperplanes. Such a situation is natural for mechanical systems with dry friction and without constraints and sticking of oscillations. To illustrate the result we prove stability of the velocity of vibration-induced displacement.

On forced oscillations in groups of interacting nonlinear systems

Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface, possibly with a boundary, in an external periodic field. We present sufficient conditions for the existence of a periodic solution for the whole system. The result is illustrated by a series of examples including a chain of strongly coupled pendulums in a periodic field.

概周期函数的均匀振荡性质

Uniform oscillation properties of almost periodic functions

本文系统研究了概周期函数的均匀振荡长度，证明了零均值标量概周期函数存在均匀振荡长度，并探讨了连续介质力学中相关函数的振荡上界，最后回顾了方形薄膜振动的未解问题。

扩展拟线性哈密顿系统的一个非振荡准则

A non oscillation criterion for extended quasi linear Hamiltonian systems

本文利用Riccati方程方法为扩展拟线性哈密顿系统建立了一个新的非振荡准则。

A topological approach to periodic oscillations related to the Liebau phenomenon

We give some sufficient conditions for existence, non-existence and localization of positive solutions for a periodic boundary value problem related to the Liebau phenomenon. Our approach is of topological nature and relies on the Krasnosel'ski\uı-Guo theorem on cone expansion and compression. Our results improve and complement earlier ones in the literature.