三阶时滞差分方程的振动性与渐进性

Oscillation and asymptotic property of cubic-order delay difference equation

研究了形如Δ3xn+ mi=1pi(n)xn-ki=0的一类三阶时滞差分方程的振动性与渐进性,得到了其解振动的2个充分条件,从而将X.H.Tang等提出的一阶形式的差分方程的振动性问题推广到三阶形式的振动性问题上.

This paper studies the oscillations and asymptotic properties of the cubicorder delay difference equation Δ3xn+mi=1pi(n)xn-ki=0, where {pi(n)} is a sequence of nonnegative real numbers, ki is positive integer, i = 1, 2, …. Two sufficient conditions for the equation mentioned above are given , which extends the results of oscillation of firstorder delay difference equation referred to by X.H.Tang.