Forced Vibrations of a Nonhomogeneous String

@article{Baldi2008ForcedVO,
  title={Forced Vibrations of a Nonhomogeneous String},
  author={Pietro Baldi and Massimiliano Berti},
  journal={SIAM J. Math. Anal.},
  year={2008},
  volume={40},
  pages={382-412}
}
We prove existence of vibrations of a nonhomogeneous string under a nonlinear time periodic forcing term in the case in which the forcing frequency avoids resonances with the vibration modes of the string (nonresonant case). The proof relies on a Lyapunov–Schmidt reduction and a Nash–Moser iteration scheme. 

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