(untitled) (Communications in Mathematical Research, 2021)
In this paper, the Dirichlet boundary value problems of the nonlinear beam equation u_tt + ∆^2u + αu + ϵϕ(t)(u + u^3 ) = 0, α > 0 in the dimension one is considered, where u(t, x) and ϕ(t) are analytic quasi-periodic functions in t, and ϵ is a small positive real-number parameter. It is proved that the above equation admits a small-amplitude quasi-periodic solution. The proof is based on an infinite dimensional KAM iteration procedure.