  We obtain multiplicity results for a class of first-order superquadratic
Hamiltonian systems and a class of indefinite superquadratic elliptic systems
which lead to the study of strongly indefinite functionals. There is no
assumption to the effect that the nonlinear terms have to satisfy the
Ambrosetti-Rabinowitz superquadratic condition. To establish the existence of
solutions, a new version of the symmetric mountain pass theorem for strongly
indefinite functionals is presented in this paper. This theorem is subsequently
applied to deal with cases where all the Palais-Smale sequences of the energy
functional may be unbounded.
