Kolmogorov–Arnold–Moser theorem for nonlinear beam equations with almost-periodic forcing

Abstract In this study, we construct a Kolmogorov–Arnold–Moser theorem regarding the existence of almost-periodic solutions for some infinitely dimensional Hamiltonian systems with almost-periodic forcing. This theorem is applied to an almost-periodically forced nonlinear beam equation with periodic boundary conditions to obtain the almost-periodic solutions u t t + ( − ∂ x x + μ ) 2 u + ψ ( ω t ) f ( u ) = 0 , μ > 0 , t ∈ R , x ∈ R , where ψ ( ω t ) is real analytic and almost periodic on t and the nonlinearity f is a real-analytic function near u = 0 with f ( 0 ) = f ′ ( 0 ) = 0 .