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

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.