Navegar

Colección

Datos Estadísticas

Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We obtain existence of T-periodic solutions to a second order system of ordinary differential equations of the form u'' + cu' + g(u) = p where c ε R; p ε C(R;R N) is T-periodic and has mean value zero, and g ε C(RN;RN) is e.g. sublinear. In contrast with a well known result by Nirenberg [6], where it is assumed that the nonlinearity g has non-zero uniform radial limits at infinity, our main result allows rapid rotations in g.

Registro:

Documento: Artículo
Título:Periodic solutions of resonant systems with rapidly rotating nonlinearities
Autor:Amster, P.; Clapp, M.
Filiación:Departamento de Matemàtica, Universidad de Buenos Aires and CONICET, Pabellón I, 1428 Buenos Aires, Argentina
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510 México DF, Mexico
Palabras clave:Leray-Schauder degree; Nonlinear systems; Periodic solutions; Rapidly rotating nonlinearities; Resonant problems
Año:2011
Volumen:31
Número:2
Página de inicio:373
Página de fin:383
DOI: http://dx.doi.org/10.3934/dcds.2011.31.373
Título revista:Discrete and Continuous Dynamical Systems
Título revista abreviado:Discrete Contin. Dyn. Syst.
ISSN:10780947
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10780947_v31_n2_p373_Amster

Referencias:

  • Alonso, J.M., Nonexistence of periodic solutions for a damped pendulum equation (1997) Differential and integral equations, 10 (6), pp. 1141-1148
  • Kannan, R., Nagle, K., Forced oscillations with rapidly vanishing nonlinearities (1991) Proc. Amer. Math. Soc., 111, pp. 385-393
  • Kannan, R., Ortega, R., Periodic solutions of pendulum-type equations (1985) J. Differential Equations, 59, pp. 123-144
  • Lazer, A., On Schauder's Fixed point theorem and forced second-order nonlinear oscillations (1968) J. Math. Anal. Appl., 21, pp. 421-425
  • Mawhin, J., An extension of a theorem of A. C. Lazer on forced nonlinear oscillations (1972) J. Math. Anal. Appl., 40, pp. 20-29
  • Nirenberg, L., Generalized degree and nonlinear problems (1971) Contributions to Nonlinear Functional Analysis, pp. 1-9. , (E. H. Zarantonello ed.), Academic Press New York
  • Ortega, R., A counterexample for the damped pendulum equation (1987) Acad. Roy. Belg. Bull. Cl. Sci., 73, pp. 405-409
  • Ortega, R., Sánchez, L., Periodic solutions of forced oscillators with several degrees of freedom (2002) Bull. London Math. Soc., 34, pp. 308-318
  • 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, pp. 2659-2665
  • Ruiz, D., Ward, J.R., Some notes on periodic systems with linear part at resonance (2004) Discrete and Continuous Dynamical Systems, 11 (2-3), pp. 337-350

Citas:

---------- APA ----------
Amster, P. & Clapp, M. (2011) . Periodic solutions of resonant systems with rapidly rotating nonlinearities. Discrete and Continuous Dynamical Systems, 31(2), 373-383.
http://dx.doi.org/10.3934/dcds.2011.31.373
---------- CHICAGO ----------
Amster, P., Clapp, M. "Periodic solutions of resonant systems with rapidly rotating nonlinearities" . Discrete and Continuous Dynamical Systems 31, no. 2 (2011) : 373-383.
http://dx.doi.org/10.3934/dcds.2011.31.373
---------- MLA ----------
Amster, P., Clapp, M. "Periodic solutions of resonant systems with rapidly rotating nonlinearities" . Discrete and Continuous Dynamical Systems, vol. 31, no. 2, 2011, pp. 373-383.
http://dx.doi.org/10.3934/dcds.2011.31.373
---------- VANCOUVER ----------
Amster, P., Clapp, M. Periodic solutions of resonant systems with rapidly rotating nonlinearities. Discrete Contin. Dyn. Syst. 2011;31(2):373-383.
http://dx.doi.org/10.3934/dcds.2011.31.373