Oscillation theorems for certain second order nonlinear difference equations

In this paper discrete inequalities are used to offer sufficient conditions for the oscillation of all solutions of the difference equation Delta(a(n)(Delta y(n))(sigma)+q(n+1)f(y(n+1)) = r(n), n greater than or equal to 0 where 0 < sigma = p/q with p, q odd integers, or p even and q odd integers. Several examples which dwell upon the importance of our results are also included. (C) 1996 Academic Press, Inc.