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Amster, P.; Mariani, M.C. "Some results on the forced pendulum equation" (2008) Nonlinear Analysis, Theory, Methods and Applications. 68(7):1874-1880
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Abstract:

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.

Registro:

Documento: Artículo
Título:Some results on the forced pendulum equation
Autor:Amster, P.; Mariani, M.C.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires, Argentina
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina
Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003-0001, United States
Palabras clave:Friction; Pendulums; Problem solving; Theorem proving; Time varying systems; Forced pendulum equation; T-periodic solutions; Nonlinear equations
Año:2008
Volumen:68
Número:7
Página de inicio:1874
Página de fin:1880
DOI: http://dx.doi.org/10.1016/j.na.2007.01.018
Título revista:Nonlinear Analysis, Theory, Methods and Applications
Título revista abreviado:Nonlinear Anal Theory Methods Appl
ISSN:0362546X
CODEN:NOAND
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v68_n7_p1874_Amster

Referencias:

  • Alonso, J., Nonexistence of periodic solutions for a damped pendulum equation (1997) Differential Integral Equations, 10, pp. 1141-1148
  • Amster, P., Mariani, M.C., Periodic solutions of the forced pendulum equation with friction (2003) Bull. Classe des Sci., pp. 7-12
  • Fournier, G., Mawhin, J., On periodic solutions of forced pendulum-like equations (1985) J. Differential Equations, 60, pp. 381-395
  • Hamel, G., Über erzwungene Schwingungen bei endlichen Amplituden (1922) Math. Ann., 86, pp. 1-13
  • Mawhin, J., Periodic oscillations of forced pendulum-like equations (1982) Lecture Notes in Math., 964, pp. 458-476. , Springer
  • Mawhin, J., The forced pendulum: A paradigm for nonlinear analysis and dynamical systems (1988) Expo. Math., 6, pp. 271-287
  • Ortega, R., A counterexample for the damped pendulum equation (1987) Bull. Classe des Sci., Ac. Roy. Belgique, LXXIII, pp. 405-409
  • Ortega, R., Serra, E., Tarallo, M., Non-continuation of the periodic oscillations of a forced pendulum in the presence of friction (2000) Proc. Amer. Math. Soc., 128 (9), pp. 2659-2665

Citas:

---------- APA ----------
Amster, P. & Mariani, M.C. (2008) . Some results on the forced pendulum equation. Nonlinear Analysis, Theory, Methods and Applications, 68(7), 1874-1880.
http://dx.doi.org/10.1016/j.na.2007.01.018
---------- CHICAGO ----------
Amster, P., Mariani, M.C. "Some results on the forced pendulum equation" . Nonlinear Analysis, Theory, Methods and Applications 68, no. 7 (2008) : 1874-1880.
http://dx.doi.org/10.1016/j.na.2007.01.018
---------- MLA ----------
Amster, P., Mariani, M.C. "Some results on the forced pendulum equation" . Nonlinear Analysis, Theory, Methods and Applications, vol. 68, no. 7, 2008, pp. 1874-1880.
http://dx.doi.org/10.1016/j.na.2007.01.018
---------- VANCOUVER ----------
Amster, P., Mariani, M.C. Some results on the forced pendulum equation. Nonlinear Anal Theory Methods Appl. 2008;68(7):1874-1880.
http://dx.doi.org/10.1016/j.na.2007.01.018