An Application of Discrete Inequality to Second Order Nonlinear Oscillation

By using some simple discrete inequalities oscillation criteria are provided for the second order difference equations Δ2yn+an+1ƒ(yn+1)=0 n∈N where the operator Δ is defined by Δyn=yn+1−yn, {an} is a real sequence. The function ƒ is such that uƒ(u)>0 for u≠0 and ƒ(u)−ƒ(v)=g(u, v)(u−v) for u, v≠0 for some nonnegative function g.