ABSTRACT
Abstract Conditions for existence of solutions bounded on the whole line Z for a weakly perturbed linear difference systems x(n + 1) = A(n)x(n) + f(n) + εA1(n)x(n) are obtained under the assumption that the unperturbed (ε = 0) linear homogeneous system has a dichotomy on both half-lines Z+ and Z− and corresponding unperturbed linear nonhomogeneous system has no solutions bounded on the whole line Z for arbitrary nonhomogeneity.
