Oscillation criteria for certain second order nonlinear difference equations

Abstract

This paper is concerned with nonlinear difference equations of the formwhere δ is the forward difference operator defined by δun−1 =un−un−1 δ2un−1= δ(δun-1) and {an} is a real sequence which is not assumed to be nonnegative. The functionfis such thatuf(u) < 0 for allu≠ 0 andf(u) −f(v) =g(u, v)(u − v), for allu, v≠ 0, and for some nonnegative functiong. Our results are not only new but also improve and generalise some recent oscillation criteria. Examples illustrating the importance of our main results are also given.