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Periodic solutions of resonant systems with rapidly rotating nonlinearities
1. | Departamento de Matemática, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires |
2. | Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510 México D.F. |
References:
[1] |
J. M. Alonso, Nonexistence of periodic solutions for a damped pendulum equation, Differential Integral Equations, 10 (1997), 1141-1148. |
[2] |
R. Kannan and K. Nagle, Forced oscillations with rapidly vanishing nonlinearities, Proc. Amer. Math. Soc., 111 (1991), 385-393.
doi: 10.1090/S0002-9939-1991-1028287-X. |
[3] |
R. Kannan and R. Ortega, Periodic solutions of pendulum-type equations, J. Differential Equations, 59 (1985), 123-144. |
[4] |
A. Lazer, On Schauder's Fixed point theorem and forced second-order nonlinear oscillations, J. Math. Anal. Appl., 21 (1968), 421-425.
doi: 10.1016/0022-247X(68)90225-4. |
[5] |
J. Mawhin, An extension of a theorem of A. C. Lazer on forced nonlinear oscillations, J. Math. Anal. Appl., 40 (1972), 20-29.
doi: 10.1016/0022-247X(72)90025-X. |
[6] |
L. Nirenberg, Generalized degree and nonlinear problems, in "Contributions to Nonlinear Functional Analysis" (E. H. Zarantonello ed.), Academic Press New York, (1971), 1-9. |
[7] |
R. Ortega, A counterexample for the damped pendulum equation, Acad. Roy. Belg. Bull. Cl. Sci., 73 (1987), 405-409. |
[8] |
R. Ortega and L. Sánchez, Periodic solutions of forced oscillators with several degrees of freedom, Bull. London Math. Soc., 34 (2002), 308-318.
doi: 10.1112/S0024609301008748. |
[9] |
R. Ortega, E. Serra and M. Tarallo, Non-continuation of the periodic oscillations of a forced pendulum in the presence of friction, Proc. Amer. Math. Soc., 128 (2000), 2659-2665.
doi: 10.1090/S0002-9939-00-05389-2. |
[10] |
D. Ruiz and J. R. Ward Jr., Some notes on periodic systems with linear part at resonance, Discrete and Continuous Dynamical Systems, 11 (2004), 337-350.
doi: 10.3934/dcds.2004.11.337. |
show all references
References:
[1] |
J. M. Alonso, Nonexistence of periodic solutions for a damped pendulum equation, Differential Integral Equations, 10 (1997), 1141-1148. |
[2] |
R. Kannan and K. Nagle, Forced oscillations with rapidly vanishing nonlinearities, Proc. Amer. Math. Soc., 111 (1991), 385-393.
doi: 10.1090/S0002-9939-1991-1028287-X. |
[3] |
R. Kannan and R. Ortega, Periodic solutions of pendulum-type equations, J. Differential Equations, 59 (1985), 123-144. |
[4] |
A. Lazer, On Schauder's Fixed point theorem and forced second-order nonlinear oscillations, J. Math. Anal. Appl., 21 (1968), 421-425.
doi: 10.1016/0022-247X(68)90225-4. |
[5] |
J. Mawhin, An extension of a theorem of A. C. Lazer on forced nonlinear oscillations, J. Math. Anal. Appl., 40 (1972), 20-29.
doi: 10.1016/0022-247X(72)90025-X. |
[6] |
L. Nirenberg, Generalized degree and nonlinear problems, in "Contributions to Nonlinear Functional Analysis" (E. H. Zarantonello ed.), Academic Press New York, (1971), 1-9. |
[7] |
R. Ortega, A counterexample for the damped pendulum equation, Acad. Roy. Belg. Bull. Cl. Sci., 73 (1987), 405-409. |
[8] |
R. Ortega and L. Sánchez, Periodic solutions of forced oscillators with several degrees of freedom, Bull. London Math. Soc., 34 (2002), 308-318.
doi: 10.1112/S0024609301008748. |
[9] |
R. Ortega, E. Serra and M. Tarallo, Non-continuation of the periodic oscillations of a forced pendulum in the presence of friction, Proc. Amer. Math. Soc., 128 (2000), 2659-2665.
doi: 10.1090/S0002-9939-00-05389-2. |
[10] |
D. Ruiz and J. R. Ward Jr., Some notes on periodic systems with linear part at resonance, Discrete and Continuous Dynamical Systems, 11 (2004), 337-350.
doi: 10.3934/dcds.2004.11.337. |
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