On the oscillation of some linear difference equations with periodic coefficients

Some linear difference equations with periodic coefficients (not necessarily nonnegative) are considered. Necessary conditions and sufficient conditions for the oscillation of the solutions are established. Conditions under which all nonoscillatory solutions tend to zero at ∞ are also presented. The results obtained are the discrete analogues of the oscillation results for some linear delay differential equations with periodic coefficients, which were given earlier by the second author [Oscillations of some delay differential equations with periodic coefficients, J. Math. Anal. Appl. 162 (1991) 452–475].