  We prove a general theorem on the existence of heteroclinic orbits in Hilbert
spaces, and present a method to reduce the solutions of some P.D.E. problems to
such orbits. In our first application, we give a new proof in a slightly more
general setting of the heteroclinic double layers (initially constructed by
Schatzman), since this result is particularly relevant for phase transition
systems. In our second application, we obtain a solution of a fouth order
P.D.E. satisfying similar boundary conditions.
