  Reference [1] established an index theory for a class of linear selfadjoint
operator equations covering both second order linear Hamiltonian systems and
first order linear Hamiltonian systems as special cases. In this paper based
upon this index theory we construct a new reduced functional to investigate
multiple solutions for asymptotically linear operator equations by Morse
theory. The functional is defined on an infinite dimensional Hilbert space, is
twice differentiable and has a finite Morse index. Investigating critical
points of this functional by Morse theory gives us a unified way to deal with
nontrivial solutions of both asymptotically second order Hamiltonian systems
and asymptotically first order Hamiltonian systems.
