### Harmonic and subharmonic solutions for suplinear Duffing equation with delay

DOI: http://dx.doi.org/10.12775/TMNA.2016.029

#### Abstract

#### Keywords

#### References

Z.B. Cheng and J.L. Ren, Periodic and subharmonic solutions for Duffing equation with singularity, Discrete Contin. Dyn. Syst. A 32 (2012), 1557–1574.

T.R. Ding, R. Iannacci and F. Zanolin, Existence and multiplicity results for periodic solution of semilinear Duffing equation, J. Differential Equations 105 (1993), 364–409.

T.R. Ding, R. Iannacci and F. Zanolin, Applications of Qualitative Methods of Ordinary Differential Equations, Higher Education Press, Beijing (2004).

W.Y. Ding, Fixed points of twist mappings and periodic solutions of ordinary differnetial equations, Acta Math. Sinica 25 (1982), 227–235.

A. Fonda, R. Manásevich and F. Zanolin, Subharmonic solutions for some secondorder differential equatins with singularities, SIAM J. Math. Anal. 24 (1993), 1294–1311.

P. Habets and G. Metzen, Existence of periodic solutins of Duffing equation, J. Differential Equations 78 (1989), 1–32.

F.F. Jiang, J.H. Shen and Y.T. Zeng, Applications of the Poincaré–Birkhoff theorem to impulsive Duffing equations at resonance, Nonlinear Anal. RWA 13 (2012), 1292–1305.

S.W. Ma and J.H. Wu, A small twist theorem and boundedness of solutions for semilinear Duffing equations at resonance, Nonlinear Anal. 67 (2007), 200–237.

X. Li, Boundedness of solution for Duffing Equations with semilinear potentials, J. Differential Equations 176 (2001), 248–268.

B. Liu, Bounded of sulutions for semilinear Duffing equations, J. Differential Equations 145 (1998), 119–144.

B. Liu, On Littlewood’s boundedness problem for sublinear Duffing equations, Trans. Amer. Math. Soc. 353 (2001), 1567–1585.

M. Del Pino and R. Manásevich, Infinitely many T-periodic solutions for a problem arising in nonlinear elasticity, J. Differential Equations 103 (1993), 260–277.

D.B. Qian, Infinity of subharmonics for asymmetric Duffing equations with the Lazer–Leach–Dancer condition, J. Differential Equations 171 (2001), 233–250.

P.J. Torres, Weak singularities may help periodic solutions to exist, J. Differential Equations 232 (2007), 277–284.

Z.H. Wang and T.T. Ma, Existence and multiplicity of periodic solutions of semilinear resonant Duffing equations with singularities, Nonlinearity 25 (2012), 279–307.

### Refbacks

- There are currently no refbacks.