Harmonic oscillators at resonance, perturbed by a non-linear friction   force
  This note is an addendum to the results of P.O. Frederickson and A.C. Lazer [1], and A.C. 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. 
Philip Korman and Yi Li
math.CA math.AP