  We analyze the stability of excitonic ground states in the two-band Hubbard
model with additional electron-phonon and Hund's rule couplings using a
combination of mean-field and variational cluster approaches. We show that both
the interband Coulomb interaction and the electron-phonon interaction will
cooperatively stabilize a charge density wave (CDW) state which typifies an
"excitonic" CDW if predominantly triggered by the effective interorbital
electron-hole attraction or a "phononic" CDW if mostly caused by the coupling
to the lattice degrees of freedom. By contrast, the Hund's rule coupling
promotes an excitonic spin density wave. We determine the transition between
excitonic charge and spin density waves and comment on a fixation of the phase
of the excitonic order parameter that would prevent the formation of a
superfluid condensate of excitons. The implications for exciton condensation in
several material classes with strongly correlated electrons are discussed.
