Asymptotic and oscillatory behavior of solutions of general nonlinear difference equations of second order

The asymptotic and oscillatory behavior of solutions of some general second -order nonlinear difference equations of the form Delta(a(n)h(y(n+1))Delta y(n)) + p(n)Delta y(n) + q(n+1)f(y(sigma(n+1))) = 0, n is an element of Z, is studied. Oscillation criteria for their solutions, when {p(n)} is of con stant sign, are established. Results are also presented for the damped-forc ed equation Delta(a(n)h(y(n+1))Delta y(n)) + p(n)Delta y(n) + q(n+1)f(y(sigma(n+1))) = e(n), n is an element of Z. Examples are inserted in the text for illustrative purposes. (C) 1998 Elsev ier Science Ltd. All rights reserved.