Abstract
We consider a family of discrete Schrödinger operators 
, 
. These operators are associated with the Hamiltonian 
of a system of two identical quantum particles (bosons) moving on the 
-dimensional lattice 
, 
, and interacting by means of a pairwise zero-range (contact) attractive potential 
. It is proved that for any 
there is a number 
which is a threshold value of the coupling constant; for 
the operator , , has a unique eigenvalue 
placed to the left of the essential spectrum. The asymptotic behaviour of is found as 
and as 
and also as 
for every value of the quasi-momentum 
belonging to the manifold 
, where 
.
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