Oscillation theorems for neutral difference equations

AbstractOscillation criteria for first order difference equations of the form Δxn + qnƒ(xn−τ) = 0 and Δ(xn +pxn−δk)+qnƒ(xn−τ) = Fn, 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} {Fn} are sequences of nonnegative real numbers and ƒ:R→R=(-∞, ∞) is continuous. Oscillation criteria for nonlinear difference equations, of sublinear as well as superlinear type, are also established