Quasi-periodic solutions of a quasi-periodically forced nonlinear beam equation

In this paper, one quasi-periodically forced nonlinear beam equation u tt + u xxxx + μ u + ε g ( ω t , x ) u 3 = 0 , μ > 0 , x ∈ [ 0 , π ] with hinged boundary conditions is considered. Here ε is a small positive parameter, g(ωt, x) is real analytic in all variables and quasi-periodic in t with a frequency vector ω = (ω1, ω2, … , ωm). It is proved that the above equation admits small-amplitude quasi-periodic solutions.