一类高阶拟线性方程的非振动准则

Nonoscillation for a High Order Quasilinear Difference Equations

考虑高阶差分方程Δ2(|Δ2yn|α-1Δ2yn)+qn|yτ(n)|β-1yτ(n)=0。α,β是正常数,{qn}n∞0是正实数列,n0∈N0={1,2,…}。limn→∞τ(n)=∞,τ(n)≤n,获得非振动解存在的充要条件。

Certain quasilinear difference equations is considered：△^2（＋△^2yn｜^（α-1）△^2yn）＋qn｜yr（n）｜^（β-1）yr（n）=0. where α,β are positive constants, {qn}n0^∞ are positive real sequences.n0∈N0{1,2,…} Nonoscillation theorems of the above equation is obtained.