We generalize to some PDEs a theorem by Nekhoroshev on the persistence of
invariant tori in Hamiltonian systems with r integrals of motion and n
degrees of freedom, r≤n. The result we get ensures the persistence of an
r-parameter family of r-dimensional invariant tori. The parameters belong
to a Cantor-like set. The proof is based on the Lyapunof-Schmidt decomposition
and on the standard implicit function theorem. Some of the persistent tori are
resonant. We also give an application to the nonlinear wave equation with
periodic boundary conditions on a segment and to a system of coupled beam
equations. In the first case we construct 2 dimensional tori, while in the
second case we construct 3 dimensional tori