Oscillation and Asymptotic Behavior of Second Order Difference Equations

AbstractThe oscillation of the second order difference equation Δ(cnΔyn) + pnyvn + 1 = 0, n = 0, 1, 2, ... (1.1) is investigated, where Δyn = yn + 1 − yn, v is a quotient of odd positive integers. Some necessary and sufficient conditions for oscillation of (1.1) with v > 1 and v < 1 are obtained. Asymptotic behavior of nonoscillatory solutions of difference equations with forced term Δ2yn − 1 + pnyn = fn, n = 1, 2, ... is considered also