Harmonic Solutions of Duffing Equation with Singularity via Time Map

Jing  Xia; Suwen  Zheng; Baohong  Lv; Caihong  Shan

doi:10.4236/am.2014.510146

Jing Xia, Suwen Zheng, Baohong Lv, Caihong Shan

Abstract: This paper is devoted to the study of second-order Duffing equation with singularity at the origin, where tends to positive infinity as , and the primitive function as . By applying the phase-plane analysis methods and Poincaré-Bohl theorem, we obtain the existence of harmonic solutions of the given equation under a kind of nonresonance condition for the time map.

Keywords: Harmonic Solutions, Duffing Equation, Singularity, Time Map, Poincaré-Bohl Theorem

Cite this paper: Xia, J. , Zheng, S. , Lv, B. and Shan, C. (2014) Harmonic Solutions of Duffing Equation with Singularity via Time Map. Applied Mathematics, 5, 1528-1534. doi: 10.4236/am.2014.510146.

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