We study a two-particle discrete Schrödinger operator
associated with a system of three particles moving on the three-dimensional cubic lattice depending on the interaction magnitude
and particles mass ratio
. We establish the essential spectrum of the two-particle discrete Schrödinger operator and prove the existence of eigenvalues located below the bottom of the essential spectrum of two-particle discrete Schrödinger operator
for all
, under the assumption that the bottom of the essential spectrum is a resonance (virtual level) of operator