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 N ω of 2 π/ ω-periodic solutions u 1,…, u n ,…, u N ω tends to +∞. The minimal period of the nth solution u n is 2 π/ nω. The proofs are based on the variational Lyapunov–Schmidt reduction (Comm. Math. Phys., to appear) and minimax arguments. 1 1 Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential Equations.
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