二阶半线性迟滞差分方程的振动准则

Oscillatory Criteria for Second-order Half-linear Delay Difference Equation

利用文献[1]中构造序列的方法，研究了二阶半线性迟滞差分方程△（rn│△un│^a-1△un）＋Pn│un-1│^a-1un-1=0, n=0,1,2…的振动性，得到了该方程的一些新的振动准则；其中实数a≥1，l为非负整数，序列{rn}^∞n=0为正实数序列，序列{Pn}^∞n=0二为非负实数序列且存在一正子序列，并且Rn=^n-1∑i=0ri^-1/a→∞（n→∞）

Making use of real sequence in [1], we study the oscillation of the second-order half-linear delay difference equation of the form △（rn│△un│^a-1△un）＋Pn│un-1│^a-1un-1=0, n=0,1,2….and established some new oscillatory criteria for the equation, where a≥ 1 is a real number, l is afixed nonnegative integer,{rn}^∞n=0 and {Pn}^∞n=0 are sequences of real numbers such that rn〉0 ,Pn〉0,{Pn}^∞n=0 has a positive subsequence, and we set Rn=^n-1∑i=0ri^-1/a→∞（n→∞）