Multiplicity of periodic solutions of nonlinear wave equations Original Research Article

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.1