Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (4): 1025-1028.doi: 10.1016/S0252-9602(14)60066-7

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HARMONIC OSCILLATORS AT RESONANCE, PERTURBED BY A NON-LINEAR FRICTION FORCE

Philip KORMAN, Yi LI   

  1. Department of Mathematical Sciences, University of Cincinnati, Cincinnati Ohio 45221-0025, USA|Department of Mathematics and Statistics, Wright State University, Dayton OH 45435, USA  
  • Received:2013-06-28 Revised:2013-12-28 Online:2014-07-20 Published:2014-07-20

Abstract:

This note is an addendum to the results of Lazer and Frederickson [1], and Lazer [4] on periodic oscillations, with linear part at resonance. We show that a small modification of the argument in [4] provides a more general result. It turns out that things are different for the corresponding Dirichlet boundary value problem.

Key words: resonance, existence of periodic solutions

CLC Number: 

  • 34C25
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