Citation: |
[1] |
J. M. Alonso and R. Ortega, Roots of unity and unbounded motions of an asymmetric oscillator, J. Differential Equations, 143 (1998), 201-220.doi: 10.1006/jdeq.1997.3367. |
[2] |
D. Bonheure, C. Fabry and D. Smets, Periodic solutions of forced isochronous oscillator at resonance, Discrete Contin. Dynam. Systems, 8 (2002), 907-930. |
[3] |
D. Bonheure and C. Fabry, Unbounded solutions of forced isochronous oscillators at resonance, Differential Integral equations, 15 (2002), 1139-1152. |
[4] |
A. Capietto and Z. Wang, Periodic solutions of Liénard equations with asymmetric nonlinearities at resonance, J. London Math. Soc., 68 (2003), 119-132.doi: 10.1112/S0024610703004459. |
[5] |
A. Capietto, W. Dambrosio and Z. Wang, Coexistence of unbounded and periodic solutions to perturbed damped isochronous oscillators at resonance, Proc. Edinburgh Math. Soc., 138A (2008), 15-32. |
[6] |
A. Capietto, W. Dambrosio, T. Ma and Z. Wang, Unbounded solutions and periodic solutions of perturbed isochronous Hamiltonian systems at resonance, Discrete Contin. Dynam. Systems, (to appear). |
[7] |
N. Dancer, Boundary value problems for weakly nonlinear ordinary differential equations, Bull. Austral. Math. Soc., 15 (1976), 321-328.doi: 10.1017/S0004972700022747. |
[8] |
P. O. Frederickson and A. C. Lazer, Necessary and sufficient damping in a second order oscillator, J. Differential Equations, 5 (1969), 262-270. |
[9] |
T. Ma and Z. Wang, Existence and infinity of periodic solutions of some second order differential equations with isochronous potentials, Z. Angew. Math. Phys., 63 (2012), 25-49.doi: 10.1007/s00033-011-0152-1. |
[10] |
T. Yoshizawa, "Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions," Springer, New York, 1975. |
[11] |
C. Fabry and A. Fonda, Nonlinear resonance in asymmetric oscillators, J. Differential Equations, 147 (1998), 58-78.doi: 10.1006/jdeq.1998.3441. |
[12] |
C. Fabry and A. Fonda, Periodic solutions of perturbed isochronous Hamiltonian systems at resonance, J. Differential Equations, 214 (2005), 299-325.doi: 10.1016/j.jde.2005.02.003. |
[13] |
C. Fabry and J. Mawhin, Oscillations of a forced asymmetric oscillators at resonance, Nonlinearity, 13 (2000), 493-505.doi: 10.1088/0951-7715/13/3/302. |
[14] |
A. Fonda and M. Garrione, Double resonance with Landesman-Lazer conditions for planar systems of ordinary differential equations, J. Differential Equations, 250 (2011), 1052-1082.doi: 10.1016/j.jde.2010.08.006. |
[15] |
A. Fonda and J. Mawhin, Planar differential systems at resonance, Adv. Diff. Eqns, 11 (2006), 1111-1133. |
[16] |
S. Fucik, "Solvability of Nonlinear Equations and Boundary Value Problems," Reidel, Boston, 1980. |
[17] |
A. C. Lazer and D. E. Leach, Bounded perturbations of forced harmonic oscillations at resonance, Ann. Mat. Pura. Appl., 82 (1969), 49-68.doi: 10.1007/BF02410787. |
[18] |
A. C. Lazer and P. J. McKenna, Existence, uniqueness and stability of oscillators in differential equations with asymmetric nonlinearities, Trans. Amer. Math. Soc., 315 (1989), 721-739.doi: 10.1090/S0002-9947-1989-0979963-1. |
[19] |
J. J. Landau and E. M. Lifshitz, "Mechanics, Course of Theoretical Physics," Vol. 1, Oxford: Pergamon, 1960. |
[20] |
Z. Wang, Periodic solutions of the second order differential equations with asymmetric nonlinearities depending on the derivatives, Discrete Contin. Dynam. Systems, 9 (2003), 751-770.doi: 10.3934/dcds.2003.9.751. |
[21] |
D. Qian, Infinity of subharmonics for asymmetric Duffing equations with the Lazer-Leach-Dancer condition, J. Differential Equations, 171 (2001), 233-250.doi: 10.1006/jdeq.2000.3847. |
[22] |
M. Krasnosel'skii and P. Zabreiko, "Geometrical Methods of Nonlinear Analysis," Springer-Verlag, 1984. |