OSCILLATION THEOREMS FOR 2ND-ORDER NEUTRAL DIFFERENCE-EQUATIONS

Oscillation criteria for the second order difference equations of the form DELTA2x(n) + q(n)f(x(n-r)) = 0 and the neutral difference equatio n DELTA2(X(n) + px(n-deltak)) + q(n)f(x(n-r)) = 0 are established. Her e DELTAx(n) = x(n+1) - x(n) is the forward difference operator, delta = +/- 1, p is a real number, tau and k are nonnegative integers, {q(n) } is a sequence of nonnegtive real numbers, and f: R --> R = (- infini ty, infinity) is continuous.