二阶自共轭中立型差分方程的振动性  

The Oscillation Behavior for Second-order Self-adjoint Neutral Difference Equations

作　　者：吕晓静[1] 田玉[1] 刘玉军[1] 

机构地区：[1]河北师范大学数学与信息科学学院,河北石家庄050016

出　　处：《河北师范大学学报（自然科学版）》2003年第1期4-7,共4页Journal of Hebei Normal University：Natural Science

基　　金：河北省自然科学基金资助项目(100139)

摘　　要：研究了具有负中立型项的二阶自共轭差分方程的振动性.在中立项系数0<p<1的情形下,利用离散的Riccati变换和函数序列的构造,给出了方程的解在不满足x(n)≤px(n—r)条件下的相关结论;然后在已有结果基础上,用反证法和分类讨论的方法,得出了差分方程解的振动性.Deal with the oscillation of the second-order self-adjoint difference equation with negative neutral term when the neutral coefficient 0 < p < 1. Several related lemmas are given by using the discrete Riccati transformation and the construction of sequence of functions, so that discuss the solutions of equation which satisfies eventually x(n)> px(n - r), then, with the help of above lemmas, the oscillatory behavior of solutions of equation are obtained. The way is to proof by contradiction and classification.

关 键 词：二阶自共轭中立型差分方程 振动性 负中立型项 离散Riccati变换 

分 类 号：O241.84[理学—计算数学]