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