Some results on the forced pendulum equation

This paper is devoted to the study of the forced pendulum equation in the presence of friction, namely u″ + a u′ + sin u = f (t) with a ∈ R and f ∈ L2 (0, T). Using a shooting type argument, we prove the existence of at least two essentially different T-periodic solutions under appropriate condition...

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Autores principales: Amster, P., Mariani, M.C.
Formato: JOUR
Materias:
Friction
Pendulums
Problem solving
Theorem proving
Time varying systems
Forced pendulum equation
T-periodic solutions
Nonlinear equations
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0362546X_v68_n7_p1874_Amster
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_0362546X_v68_n7_p1874_Amster
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spelling todo:paper_0362546X_v68_n7_p1874_Amster2023-10-03T15:27:19Z Some results on the forced pendulum equation Amster, P. Mariani, M.C. Friction Pendulums Problem solving Theorem proving Time varying systems Forced pendulum equation T-periodic solutions Nonlinear equations This paper is devoted to the study of the forced pendulum equation in the presence of friction, namely u″ + a u′ + sin u = f (t) with a ∈ R and f ∈ L2 (0, T). Using a shooting type argument, we prove the existence of at least two essentially different T-periodic solutions under appropriate conditions on T and f. We also prove the existence of solutions decaying with a fixed rate α ∈ (0, 1) by the Leray-Schauder theorem. Finally, we prove the existence of a bounded solution on [0, + ∞) using a diagonal argument. © 2007 Elsevier Ltd. All rights reserved. Fil:Amster, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Mariani, M.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0362546X_v68_n7_p1874_Amster
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Friction
Pendulums
Problem solving
Theorem proving
Time varying systems
Forced pendulum equation
T-periodic solutions
Nonlinear equations
spellingShingle Friction
Pendulums
Problem solving
Theorem proving
Time varying systems
Forced pendulum equation
T-periodic solutions
Nonlinear equations
Amster, P.
Mariani, M.C.
Some results on the forced pendulum equation
topic_facet Friction
Pendulums
Problem solving
Theorem proving
Time varying systems
Forced pendulum equation
T-periodic solutions
Nonlinear equations
description This paper is devoted to the study of the forced pendulum equation in the presence of friction, namely u″ + a u′ + sin u = f (t) with a ∈ R and f ∈ L2 (0, T). Using a shooting type argument, we prove the existence of at least two essentially different T-periodic solutions under appropriate conditions on T and f. We also prove the existence of solutions decaying with a fixed rate α ∈ (0, 1) by the Leray-Schauder theorem. Finally, we prove the existence of a bounded solution on [0, + ∞) using a diagonal argument. © 2007 Elsevier Ltd. All rights reserved.
format JOUR
author Amster, P.
Mariani, M.C.
author_facet Amster, P.
Mariani, M.C.
author_sort Amster, P.
title Some results on the forced pendulum equation
title_short Some results on the forced pendulum equation
title_full Some results on the forced pendulum equation
title_fullStr Some results on the forced pendulum equation
title_full_unstemmed Some results on the forced pendulum equation
title_sort some results on the forced pendulum equation
url http://hdl.handle.net/20.500.12110/paper_0362546X_v68_n7_p1874_Amster
work_keys_str_mv AT amsterp someresultsontheforcedpendulumequation
AT marianimc someresultsontheforcedpendulumequation
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