Work

Periodic solutions of the forced conservative pendulum with relativistic acceleration and derivative dependent coefficient

Year: 2025

Type: article

Abstract: We prove that the periodic problem for the forced pendulum equation with relativistic acceleration and derivative dependent coefficient ( u ′ 1 − u ′ 2 ) ′ + a 1 − u ′ 2 sin ⁡ u = f ( t ) , u ( 0 ) = u ( T ) , u ′ ( 0 ) = u ′ ( T ) , has at least two geometrically distinct solutions when f has mean value zero. After showing that the problem is the Euler-Lagrange equation of some functional I defined when | u ′ | ∞ < 1 , we extend I into a functional I R defined on the Sobolev space H T 1 whose critical points are critical points of I . We then apply a multiplicity theorem based on Lusternik-Schnirelman category to obtain the existence of two geometrically distinct critical points of I R .

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2025.113965

Authors: P. Amster, J.A. Cid, J. Mawhin

Institutions: Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad de Buenos Aires, Universidade de Vigo, UCLouvain

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Ministerio de Ciencia, Innovación y Universidades, Ministerio de Ciencia e Innovación, European Regional Development Fund, Agencia Estatal de Investigación