一类齐次常系数线性差分方程的探究

An Exploratory Research of Homogeneous Linear Difference Equations with Constant Coefficients

在给出齐次常系数线性差分方程一般解的前提下,针对系数矩阵为三对角齐次常系数线性差分方程a·xj+b·xj_c·xj-1=o,j=1,2,…,n-1,a,b,c≠0 且 x0=xn=0的情形,给出其一般解形式并严格论证该解的存在,同时给出一推论的证明.

This paper gives the general solutions of the homogeneous linear difference equations with constant coeffcients firstly, as the case is that the matrix of coefficients is the tridiagonal matrix in the homogeneous linear difference equations with eontant coefficients,the question format is：a·xj＋b·xj_c·xj-1=o,j=1,2,…,n-1,a,b,c≠0, and x0 = xn = O,let and ,giving secondly the general solutions form and proving rigidly existence theorem of the question solutions,at the same time,refering the proof of one of the lemmas appled this method.