A result on quasi-periodic solutions of a nonlinear beam equation with a quasi-periodic forcing term

In this paper, a quasi-periodically forced nonlinear beam equation u(tt) + u(xxxx) + mu u + epsilon phi(t)h(u) = 0 with hinged boundary conditions is considered, where mu > 0, e is a small positive parameter, phi is a real analytic quasi-periodic function in t with a frequency vector omega = (omega(1), omega(2), ... , omega(m)), and the nonlinearity h is a real analytic odd function of the form h(u) = eta(1u+eta 2(r)over bar) ((r)over bar +)(+ 1u2) Sigma k >=((r)over bar + 1) u (2k+1), eta(1), eta(2(r)over bar + 1) not equal 0, (r)over bar is an element of N. The above equation admits a quasi- periodic solution.