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Cantor families of periodic solutions for completely resonant wave equations

Abstract

We present recent existence results of Cantor families of small amplitude periodic solutions for completely resonant nonlinear wave equations. The proofs rely on the Nash-Moser implicit function theory and variational methods.

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Berti, M., Bolle, P. Cantor families of periodic solutions for completely resonant wave equations. Front. Math. China 3, 151–165 (2008). https://doi.org/10.1007/s11464-008-0011-3

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Keywords

  • Nonlinear wave equation
  • infinite dimensional Hamiltonian system
  • periodic solution
  • variational method
  • Lyapunov-Schmidt reduction
  • small divisor
  • Nash-Moser Theorem

MSC

  • 35L05
  • 37K50
  • 58E05