Oscillation of a Certain Class of Third Order Nonlinear Difference Equations

In this paper, we are concerned with oscillation of the nonlinear difference equation Δ(cn[Δ(dnΔxn)]^γ)+qnf(xg(n))=0, n≥n0, where γ 0 is the quotient of odd positive integers, cn, dn and qn are positive sequences of real numbers, g(n) is a sequence of nonnegative integers and f∈C(R,R) such that uf(u) 0 for u≠0. We establish some new sufficient conditions for oscillation by employing the Riccati substitution and the analysis of the associated Riccati difference inequality. Our results extend and improve some previously obtained ones. Some examples are considered to illustrate the main results.