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Harmonic Solutions of Duffing Equation with Singularity via Time Map
Department of Fundamental Courses, Academy of Armored Force Engineering, Beijing, China
Department of Fundamental Courses, Academy of Armored Force Engineering, Beijing, China
Department of Fundamental Courses, Academy of Armored Force Engineering, Beijing, China
Department of Fundamental Courses, Academy of Armored Force Engineering, Beijing, China
- 1 Department of Fundamental Courses, Academy of Armored Force Engineering, Beijing, China
- 2 Department of Fundamental Courses, Academy of Armored Force Engineering, Beijing, China
- 3 Department of Fundamental Courses, Academy of Armored Force Engineering, Beijing, China
- 4 Department of Fundamental Courses, Academy of Armored Force Engineering, Beijing, China
Applied Mathematics·Volume 05 (2014)·Pages 1528–1534·Published 22 May 2014·DOI10.4236/am.2014.510146
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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.
KeywordsHarmonic SolutionsDuffing EquationSingularityTime MapPoincaré-Bohl Theorem
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