Oscillation of second-order perturbed nonlinear difference equations

Using the Riccati transformation techniques we will establish some new oscillation criteria for the second-order perturbed nonlinear difference equation Delta(a(n-1) (Deltax(n-1))(gamma)) + F(n, x(n)) = G(n, x(n), Deltax(n)), n greater than or equal to 1 where gamma > 0 is a quotient of odd positive integers. Some comparison between our theorems and those previously known results are indicated. Examples are interested in the text to illustrate the relevance of our results. (C) 2002 Elsevier Inc. All rights reserved.