Periodic solutions of a semilinear Euler-Bernoulli beam equation with variable coefficients

Abstract

This paper is devoted to the study of periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients. Such mathematical model may be described the infinitesimal, free, undamped in-plane bending vibrations of a thin straight elastic beam. When the frequency $\omega =\frac{2\pi }{T}$ is rational, some properties of the beam operator with variable coefficients are investigated. We obtain the existence of periodic solutions when the nonlinear term is monotone and bounded.

References in corpus (3)

• A KAM algorithm for the resonant non--linear Schrödinger equation
• KAM for reversible derivative wave equations
• The Existence of Periodic Solutions for Nonlinear Beam Equations on ${\mathbb{T}}^d$ by a Para-differential Method