Oscillation theorems for second order neutral difference equations

摘要

Oscillation criteria for the second order difference equations of the form Δ2xn + qnf(xn – r) = 0 and the neutral difference equation Δ2(xn + pxn – δk) + qnf(xn – r) = 0 are established. Here Δxn = xn + 1 − xn is the forward difference operator, δ = ±1, p is a real number, τ and k are nonnegative integers, {qn} is a sequence of nonnegtive real numbers, and f: R → R = (- ∞, ∞) is continuous.