ABSTRACT
We will find periodic solutions by using Morse theory to study the crit ical points of the action functional e# • The main difficulty is that such functional is strongly indefinite, so Morse theory cannot be applied di rectly: we have seen that the Morse relations do not detect critical points with infinite Morse index. Several different approaches have been developed in order to overcome this difficulty. Conley and Zehnder [CZ84] used a sort of Lyapunov-Schmidt method called saddle point reduction, introduced by Amann [Ama79]. A drawback of this approach is that one has to assume D2H to be bounded. Other methods, based on generalized cohomology theories or on a Morse homology approach, are briefly described in section 5.4.
