一类二阶非线性差分方程的振动准则

Oscillation criteria for a kind of second-order nonlinear difference equation

运用差分方程、有理增函数的性质以及文献[1]中的定理证明方法,对一类二阶非线性差分方程解的振动性进行了研究,获得了该方程解振动的一个定理和两个推论。通过判断有理函数的增减性来研究该方程解的振动性,大大地简化了其定理的证明过程,所得结果推广和改进了文献[1]中的相应结果。

The quality of difference equation, the quality of increasing rational function, and the theorem method of prove in literature[4] are referred to in investigating the oscillation of a kind second-order nonlinear difference equation. One theorem and two infers of the equation in which it＇s solutions are oscillation are obtained. The thermo prove is predigested by judging the increasing or the decreasing quality of the rational function in order to investigate it. Ours results generalize and improve some known results of those in literature[3].