Differential and Integral Equations

On the relativistic pendulum-type equation

Antonio Ambrosetti and David Arcoya

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

Abstract

In the first part of this paper, we consider the equation $$ \Big ( \frac{u'}{\sqrt{1-u'^2}} \Big )'+F'(u)=0 $$ modeling, if $F'(u)=\sin u$, the motion of the free relativistic planar pendulum. Using critical point theory for non-smooth functionals, we prove the existence of non-trivial $T$ periodic solutions provided $T$ is sufficiently large.

In the second part, we show the existence of periodic solutions to the free and forced relativistic spherical pendulum, where $F'$ is substituted by $$ F'(u)-h^2\, G'(u)\sim \sin u -h^2 \frac {\cos u}{\sin^3u} , \ \ \ h\in \mathbb R . $$

Article information

Source
Differential Integral Equations, Volume 33, Number 3/4 (2020), 91-112.

Dates
First available in Project Euclid: 21 March 2020

Permanent link to this document
https://projecteuclid.org/euclid.die/1584756014

Mathematical Reviews number (MathSciNet)
MR4079784

Subjects
Primary: 34B15: Nonlinear boundary value problems 49J40: Variational methods including variational inequalities [See also 47J20] 35Q75: PDEs in connection with relativity and gravitational theory

Citation

Ambrosetti, Antonio; Arcoya, David. On the relativistic pendulum-type equation. Differential Integral Equations 33 (2020), no. 3/4, 91--112. https://projecteuclid.org/euclid.die/1584756014


Export citation