Subharmonic Solutions with Prescribed Minimal Period of a Forced Pendulum Equation with Impulses

  • Fanchao Kong


This paper is mainly concerned with a forced pendulum equation with impulses and the length of the pendulum is variable. The main tool utilized to establish our results on the subharmonic solutions with prescribed minimal period is the theorem of the least action principle due to Mawhin and Willem. As an application, three examples are given, and the corresponding numerical subharmonic solutions for the examples are obtained by applying Matlab software. Some results in the literature can be generalized and improved.


Subharmonic solution Forced pendulum equation Impulses Prescribed minimal period The least action principle 

Mathematics Subject Classification




The authors thank the anonymous reviewers for their insightful suggestions which improved this work significantly. In particular, the authors express the sincere gratitude to Prof. Zhiguo Luo and Prof. Jianli Li (Hunan Normal University) for the helpful discussion when this work was being carried out.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and Big DataAnhui University of Science and TechnologyHuainanP.R. China

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