  We describe a variational approach to a notion of Hamiltonian delay
equations. Our delay Hamiltonians are of product form. We consider several
examples. For closed symplectically aspherical symplectic manifolds
$(M,\omega)$ we prove that for generic delay Hamiltonians the number of
1-periodic solutions of the Hamiltonian delay equation is at least the sum of
the Betti numbers of $M$, extending the proof of the Arnold conjecture to the
case with delay.
