三阶非线性差分方程的非振动性定理

Nonoscillation Theorems for Third Order Nonlinear Difference Equations

给出了一类三阶非线性差分方程Δa(pnΔa2yn)+qnΔa2yn=f(n,yn,Δbyn,Δ2byn)的所有解都是非振动解的充分条件,其中Δx为广义差分算子:Δxyn=yn+1-xyn,x=a,b,a>0,b∈(9).所得结论推广和改进了已有文献的结果.

In this paper,sufficient conditions are obtained for nonoscillation of all solutions of a class of third order nonlinear difference equations of the formΔa（pnΔ2ayn）＋qnΔ2ayn=f（n,yn,Δbyn,Δ2byn）involving the generalized difference operator Δx which is defined as Δxyn=yn＋1-xyn,x=a,b,and a0,b∈R.The obtained theorems extend and improve some recent results.