OSCILLATION THEOREMS FOR NEUTRAL DIFFERENCE-EQUATIONS

Oscillation criteria for first order difference equations of the form DELTA x(n) + q(n) f(x(n-tau)) = 0 and DELTA (x(n) + px(n-deltak)) + q( n) f(x(n-tau)) = F(n), are established. Here DELTA x(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)}, {F(n)} are sequences of nonnegative real numbers and f : R --> R = (-infinity, infinity) is co ntinuous. Oscillation criteria for nonlinear difference equations, of sublinear as well as superlinear type, are also established.