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March/April 2020 On the relativistic pendulum-type equation
Antonio Ambrosetti, David Arcoya
Differential Integral Equations 33(3/4): 91-112 (March/April 2020).

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 $$ F'(u)-h^2\, G'(u)\sim \sin u -h^2 \frac {\cos u}{\sin^3u} , \ \ \ h\in \mathbb R . $$

Citation

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Antonio Ambrosetti. David Arcoya. "On the relativistic pendulum-type equation." Differential Integral Equations 33 (3/4) 91 - 112, March/April 2020.

Information

Published: March/April 2020
First available in Project Euclid: 21 March 2020

zbMATH: 07217165
MathSciNet: MR4079784

Subjects:
Primary: 34B15, 35Q75, 49J40

Rights: Copyright © 2020 Khayyam Publishing, Inc.

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Vol.33 • No. 3/4 • March/April 2020
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