It is a rule of thumb that time delay tends to destabilize any dynamical system. This is not
true, however, in the case of delayed oscillators, which serve as mechanical models for …

The history of the linear time-delayed and time-periodic oscillator demonstrates how stability
theory has developed from the damped oscillator to the delayed Mathieu equation. Based …

In a first part we discuss the well-known problem of the motion of a star in a general non-
axisymmetric 2D galactic potential by means of a very simple but almost universal system …

Several years ago, I was intensively studying semilinear biharmonic elliptic equations, a
topic quite far away from suspension bridges. In 2009, I was invited at a conference in …

Linear mechanical systems with time-modulated parameters can harbor oscillations with
amplitudes that grow or decay exponentially with time due to the phenomenon of parametric …

For piecewise-smooth maps, new dynamics can be created by varying parameters such that
a fixed point collides with a surface on which the map is nonsmooth. If the map is continuous …

We model the roadway of a suspension bridge as a thin rectangular plate and we study in
detail its oscillating modes. The plate is assumed to be hinged on its short edges and free on …

A simple example is considered of Hill's equation ̈ x+(a^ 2+ bp (t)) x= 0, where the forcing
term p, instead of periodic, is quasi-periodic with two frequencies. A geometric exploration is …

This paper is a continuation of Zhang [M. Zhang, Continuity in weak topology: Higher order
linear systems of ODE, Sci. China Ser. A 51 (2008) 1036–1058; M. Zhang, Extremal values …

Given a 1-periodic real potential q∈ L1 (R/Z). We use λ0 (q) to denote the smallest 1-
periodic eigenvalue of the Hill's equation x ″+(λ+ q (t)) x= 0. Let B1 [r] be the ball centered …