Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (4): 761-772.

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Periodic Solutions of a Class of Nonlinear Hill's Type Equations with Bounded Restoring Force

Chao Wang()   

  1. School of Mathematics and Statistics, YanCheng Teacher's University, Jiangsu Yancheng 224001
  • Received:2018-01-15 Online:2019-08-26 Published:2019-09-11
  • Supported by:
    the NSFC(11571249);the Natural Science Fundation of Jiangsu Province(BK20171275)


In this pater, we study the existence and multiplicity of the periodic solutions of a class of Hill's type equations with bounded restoring force. We prove the existence of infinite of subharmonic solutions when the weight is positive. We also consider the existence, multiplicity and dense distribution of symmetric periodic solutions in case of even and periodic weight functions.

Key words: Hill's type equation, Weight functions, Bounded restoring force, Sub-harnomic solutions, Symmetric periodic solutions

CLC Number: 

  • O175.14