-
Previous Article
On $C^0$-variational solutions for Hamilton-Jacobi equations
- DCDS Home
- This Issue
-
Next Article
Exponentially small splitting of separatrices in the perturbed McMillan map
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.
|
[2] |
R. Kannan and K. Nagle, Forced oscillations with rapidly vanishing nonlinearities,, Proc. Amer. Math. Soc., 111 (1991), 385.
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.
|
[4] |
A. Lazer, On Schauder's Fixed point theorem and forced second-order nonlinear oscillations,, J. Math. Anal. Appl., 21 (1968), 421.
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.
doi: 10.1016/0022-247X(72)90025-X. |
[6] |
L. Nirenberg, Generalized degree and nonlinear problems,, in, (1971), 1.
|
[7] |
R. Ortega, A counterexample for the damped pendulum equation,, Acad. Roy. Belg. Bull. Cl. Sci., 73 (1987), 405.
|
[8] |
R. Ortega and L. Sánchez, Periodic solutions of forced oscillators with several degrees of freedom,, Bull. London Math. Soc., 34 (2002), 308.
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.
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.
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.
|
[2] |
R. Kannan and K. Nagle, Forced oscillations with rapidly vanishing nonlinearities,, Proc. Amer. Math. Soc., 111 (1991), 385.
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.
|
[4] |
A. Lazer, On Schauder's Fixed point theorem and forced second-order nonlinear oscillations,, J. Math. Anal. Appl., 21 (1968), 421.
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.
doi: 10.1016/0022-247X(72)90025-X. |
[6] |
L. Nirenberg, Generalized degree and nonlinear problems,, in, (1971), 1.
|
[7] |
R. Ortega, A counterexample for the damped pendulum equation,, Acad. Roy. Belg. Bull. Cl. Sci., 73 (1987), 405.
|
[8] |
R. Ortega and L. Sánchez, Periodic solutions of forced oscillators with several degrees of freedom,, Bull. London Math. Soc., 34 (2002), 308.
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.
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.
doi: 10.3934/dcds.2004.11.337. |
[1] |
Alexander Krasnosel'skii. Resonant forced oscillations in systems with periodic nonlinearities. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 239-254. doi: 10.3934/dcds.2013.33.239 |
[2] |
Diego Averna, Nikolaos S. Papageorgiou, Elisabetta Tornatore. Multiple solutions for nonlinear nonhomogeneous resonant coercive problems. Discrete & Continuous Dynamical Systems - S, 2018, 11 (2) : 155-178. doi: 10.3934/dcdss.2018010 |
[3] |
Paul Deuring, Stanislav Kračmar, Šárka Nečasová. Linearized stationary incompressible flow around rotating and translating bodies -- Leray solutions. Discrete & Continuous Dynamical Systems - S, 2014, 7 (5) : 967-979. doi: 10.3934/dcdss.2014.7.967 |
[4] |
Xiaojun Chang, Yong Li. Rotating periodic solutions of second order dissipative dynamical systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 643-652. doi: 10.3934/dcds.2016.36.643 |
[5] |
Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu. Bifurcation of positive solutions for nonlinear nonhomogeneous Robin and Neumann problems with competing nonlinearities. Discrete & Continuous Dynamical Systems - A, 2015, 35 (10) : 5003-5036. doi: 10.3934/dcds.2015.35.5003 |
[6] |
D. Wirosoetisno. Navier--Stokes equations on a rapidly rotating sphere. Discrete & Continuous Dynamical Systems - B, 2015, 20 (4) : 1251-1259. doi: 10.3934/dcdsb.2015.20.1251 |
[7] |
Jean Mawhin. Multiplicity of solutions of variational systems involving $\phi$-Laplacians with singular $\phi$ and periodic nonlinearities. Discrete & Continuous Dynamical Systems - A, 2012, 32 (11) : 4015-4026. doi: 10.3934/dcds.2012.32.4015 |
[8] |
Adriana Buică, Jean–Pierre Françoise, Jaume Llibre. Periodic solutions of nonlinear periodic differential systems with a small parameter. Communications on Pure & Applied Analysis, 2007, 6 (1) : 103-111. doi: 10.3934/cpaa.2007.6.103 |
[9] |
D. Motreanu, V. V. Motreanu, Nikolaos S. Papageorgiou. Nonautonomous resonant periodic systems with indefinite linear part and a nonsmooth potential. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1401-1414. doi: 10.3934/cpaa.2011.10.1401 |
[10] |
Boumediene Abdellaoui, Daniela Giachetti, Ireneo Peral, Magdalena Walias. Elliptic problems with nonlinear terms depending on the gradient and singular on the boundary: Interaction with a Hardy-Leray potential. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 1747-1774. doi: 10.3934/dcds.2014.34.1747 |
[11] |
Jaume Llibre, Y. Paulina Martínez, Claudio Vidal. Linear type centers of polynomial Hamiltonian systems with nonlinearities of degree 4 symmetric with respect to the y-axis. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 887-912. doi: 10.3934/dcdsb.2018047 |
[12] |
Zhenguo Liang, Jiansheng Geng. Quasi-periodic solutions for 1D resonant beam equation. Communications on Pure & Applied Analysis, 2006, 5 (4) : 839-853. doi: 10.3934/cpaa.2006.5.839 |
[13] |
Tiantian Ma, Zaihong Wang. Periodic solutions of Liénard equations with resonant isochronous potentials. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1563-1581. doi: 10.3934/dcds.2013.33.1563 |
[14] |
Zalman Balanov, Meymanat Farzamirad, Wieslaw Krawcewicz, Haibo Ruan. Applied equivariant degree. part II: Symmetric Hopf bifurcations of functional differential equations. Discrete & Continuous Dynamical Systems - A, 2006, 16 (4) : 923-960. doi: 10.3934/dcds.2006.16.923 |
[15] |
E. N. Dancer. Some bifurcation results for rapidly growing nonlinearities. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 153-161. doi: 10.3934/dcds.2013.33.153 |
[16] |
Xiaohong Li, Fengquan Li. Nonexistence of solutions for nonlinear differential inequalities with gradient nonlinearities. Communications on Pure & Applied Analysis, 2012, 11 (3) : 935-943. doi: 10.3934/cpaa.2012.11.935 |
[17] |
Marc Henrard. Homoclinic and multibump solutions for perturbed second order systems using topological degree. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 765-782. doi: 10.3934/dcds.1999.5.765 |
[18] |
Benjamin B. Kennedy. A state-dependent delay equation with negative feedback and "mildly unstable" rapidly oscillating periodic solutions. Discrete & Continuous Dynamical Systems - B, 2013, 18 (6) : 1633-1650. doi: 10.3934/dcdsb.2013.18.1633 |
[19] |
Yutong Chen, Jiabao Su. Resonant problems for fractional Laplacian. Communications on Pure & Applied Analysis, 2017, 16 (1) : 163-188. doi: 10.3934/cpaa.2017008 |
[20] |
P.E. Kloeden. Pitchfork and transcritical bifurcations in systems with homogeneous nonlinearities and an almost periodic time coefficient. Communications on Pure & Applied Analysis, 2004, 3 (2) : 161-173. doi: 10.3934/cpaa.2004.3.161 |
2018 Impact Factor: 1.143
Tools
Metrics
Other articles
by authors
[Back to Top]