  We consider a multi-polaron model obtained by coupling the many-body
Schr\"odinger equation for N interacting electrons with the energy functional
of a mean-field crystal with a localized defect, obtaining a highly non linear
many-body problem. The physical picture is that the electrons constitute a
charge defect in an otherwise perfect periodic crystal. A remarkable feature of
such a system is the possibility to form a bound state of electrons via their
interaction with the polarizable background. We prove first that a single
polaron always binds, i.e. the energy functional has a minimizer for N=1. Then
we discuss the case of multi-polarons containing two electrons or more. We show
that their existence is guaranteed when certain quantized binding inequalities
of HVZ type are satisfied.
