We prove multiplicity of small amplitude periodic solutions, with fixed frequency ω, of completely resonant wave equations with general nonlinearities. As ω→1 the number Nω of 2π/ω-periodic solutions u1,…,un,…,uNω tends to +∞. The minimal period of the nth solution un is 2π/nω. The proofs are based on the variational Lyapunov–Schmidt reduction (Comm. Math. Phys., to appear) and minimax arguments.
Multiplicity of periodic solutions of nonlinear wave equations / Berti, M.; Bolle, P.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 56:7(2004), pp. 1011-1046. [10.1016/j.na.2003.11.001]
Multiplicity of periodic solutions of nonlinear wave equations
Berti, M.;
2004-01-01
Abstract
We prove multiplicity of small amplitude periodic solutions, with fixed frequency ω, of completely resonant wave equations with general nonlinearities. As ω→1 the number Nω of 2π/ω-periodic solutions u1,…,un,…,uNω tends to +∞. The minimal period of the nth solution un is 2π/nω. The proofs are based on the variational Lyapunov–Schmidt reduction (Comm. Math. Phys., to appear) and minimax arguments.File in questo prodotto:
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