AN APPLICATION OF DISCRETE INEQUALITY TO 2ND-ORDER NONLINEAR OSCILLATION

By using some simple discrete inequalities oscillation criteria are pr ovided for the second order difference equations Delta(2)y(n) + a(n+1) f(y(n+1)) = 0, n epsilon N, where the operator Delta is defined by Del ta y, = y(n+1) - y(n), {a(n)} is a real sequence. The function f is su ch that uf(u) > 0 for u not equal 0 and f(u) - f(v) = g(u, v)(u - v) f or u, v not equal 0 for some nonnegative function g. (C) 1994 Academic Press, Inc.