Bounded and periodic solutions to the linear first-order difference equation on the integer domain

Abstract

The existence of bounded solutions to the linear first-order difference equation on the set of all integers is studied. Some sufficient conditions for the existence of solutions converging to zero when n→ − ∞ , as well as when n→ + ∞ , are also given. For the case when the coefficients of the equation are periodic, the long-term behavior of non-periodic solutions is studied.