On the count and the classification of periodic solutions to forced pendulum-type equations
type: Item
instance of: scholarly article
title: On the count and the classification of periodic solutions to forced pendulum-type equations
zbMATH Open document ID: 1023.34037
author: M. Calanchi
author: Massimo Tarallo
published in: Differential and Integral Equations
publication date: 2000-05-29T00:00:00Z
review text: The pendulum-type problem of the form \[ \ddot {u}+V'(u(t)) = h(t) +\lambda , \] \(u\) is \(T\)-periodic, \(\lambda \in \mathbb{R}\), is studied under some assumptions on \(T\) and the forcing \(h\). The main assumption is \(\max V'' <(\frac {2\pi }{T})^2\) and that \(V'\) is a Morse function with distinct critical values. A one-to-one correspondence of solutions to the present problem to an auxiliary one for the so-called reduction function is shown. For the auxiliary equation, the number of its pre-images describes the number of the solutions to the original problem and this is the main tool for the considerations in the paper.
reviewed by: Štefan Schwabik
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 47J30
zbMATH DE Number: 1453646
zbMATH Keywords: Morse function
zbMATH Keywords: periodic solutions
zbMATH Keywords: forced pendulum-type equations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1453646