关于变系数线性方程组零解的稳定性的某些反例的构造方法

On the Constrution Method for Counter Examples of the Zero Solution Stabilty of Linear Equation System With Variable Confidents

考察线性常微分方程组 X=a_(11)(t)x+a_(12)(t)y,y=a_(21)(t)X+a_(22)(t)y。设a_(11)+a_(22)=p=常数,a_(11)a_(22)-a_(12)a_(21)=q=常数,本文首先在上述方程的一个特解x=ψ_1(t),y=ψ_2(t)的条件下,给出了系数a_(ij)(i,j=1,2)的公式和求通解的公式。其次,利用这些结果,给出了构造某些方程组的简便方法,这些方程组可以说明具有变系数的线性组的零解的稳定性质不依赖于方程组的特征方程的根,文内特别讨论了构造具有有界系数的方程组的方法.

Consider the system of equationsx = a11(t)x + a12(t)y,y = a21(t)x + a22(t)yWith the following conditions : a11+a22 = p = const and a11a22 - a21a12 = q = con-st.In this paper,first of all,the formulas of determing the confficients aij (i, j=1 , 2 )of equation and the formulas of finding the general solution of (1.1) are provided,if a particular solution x = 1 (t) ,y = 2(t) of (1.1) is kno-wn In the next place,using these results,the simple construction method of eguation systems are found.The zero solution stability of these systems doesn't depend on the roots of characteristic equation of the system.In the paqer,the construction method of systems with bounded coefficients are particularity dis-cussed.