一类二阶拟线性差分方程的非振动性定理

NON-OSCILLATION THEOREMS FOR A CLASS OF SECOND ORDER QUASILINEAR DIFFERENCE EQUATION

研究了二阶拟线性差分方程Δ(pnφ(Δxn) ) +f(n ,xn) =0的渐近性 ,并给出了当任给 k≠ 0 , ∞n =n0φ-1kpn =∞时此方程存在Ac∞ ,A0c 型非振动解的充要条件以及存在A0 ∞

In this paper, the nonoscillatory properties of quasilinear difference equation of second order Δ(p nφ(Δx n))+f(n,x n)=0 are considered. Under the hypothese for any k≠0 , ∞]n=n 0n=n 0φ -1k]p np n=∞, we give the iif conditions of the Equation which exists nonoscillatory solutions belonging to the type of A c ∞ and A 0 c, and the sufficient conditions of the Equation which exists nonoscillatory solutions beloning to the type of A 0 ∞.