References
- J. M. Alonso and R. Ortega, Roots of unity and unbounded motions of an asymmetric oscillator, J. Differential Equations 143 (1998), no. 1, 201-220. https://doi.org/10.1006/jdeq.1997.3367
- A. Capietto, W. Dambroslo, and Z. Wang, Coexistence of unbounded and periodic so-lutions to perturbed damped isochronous oscillators at resonance, Proc. Roy. Soc. Edin-burgh Sect. A 138 (2008), no. 1, 15-32. https://doi.org/10.1017/S030821050600062X
- A. Capietto and Z. Wang, Periodic solutions of Lienard equations with asymmetric nonlinearities at resonance, J. London Math. Soc. (2) 68 (2003), no. 1, 119-132. https://doi.org/10.1112/S0024610703004459
- T. Ding, Nonlinear oscillations at a point of resonance, Sci. Sinica Ser. A 25 (1982), no. 9, 918-931.
- C. Fabry and A. Fonda, Nonlinear resonance in asymmetric oscillators, J. Differential Equations 147 (1998), no. 1, 58-78.
- C. Fabry and J. Mawhin, Oscillations of a forced asymmetric oscillator at resonance, Nonlinearity 13 (2000), no. 3, 493-505. https://doi.org/10.1088/0951-7715/13/3/302
- A. Fonda, Positively homogeneous Hamiltonian systems in the plane, J. Differential Equations 200 (2004), no. 1, 162-184. https://doi.org/10.1016/j.jde.2004.02.001
- A. Fonda and J. Mawhin, Planar differential systems at resonance, Adv. Differential Equations 11 (2006), no. 10, 1111-1133.
- N. G. Lloyd, Degree Theory, University Press, Cambridge, 1978.
- J. Massera, The existence of periodic solutions of systems of differential equations, Duke Math. J. 17 (1950), 457-475. https://doi.org/10.1215/S0012-7094-50-01741-8
- R. Ortega, Asymmetric oscillators and twist mappings, J. London Math. Soc. (2) 53 (1996), no. 2, 325-342. https://doi.org/10.1112/jlms/53.2.325
- Z.Wang, Coexistence of unbounded solutions and periodic solutions of Lienard equations with asymmetric nonlinearities at resonance, Sci. China Ser. A 50 (2007), no. 8, 1205-1216. https://doi.org/10.1007/s11425-007-0070-z
- X. Yang, Unboundedness of solutions of planar Hamiltonian systems. Differential & difference equations and applications, 1167-1176, Hindawi Publ. Corp., New York, 2006.
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