Almost periodic solutions for a class of higher-dimensional beam equations

In this paper, we show that there are many almost periodic solutions corresponding to full- dimensional invariant tori for higher- dimensional beam equations with Fourier multiplier u(tt) + (- Delta + M xi)(2) u + f (u) = 0, subject to periodic boundary conditions, where the nonlinearity f is a real-analytic function near u = 0 with f (0) = f '(0) = 0. The proof is based on an improved infinite- dimensional KAM theorem.