摘要
微分方程组的零解对部分变元的稳定性,文[1]、[2]关于常系数线性微分方程组作了研究,已有了结果,文[2]又推广了线性微分方程组的零解的稳定性与一切解的有界性等价的定理。我们在这里给出一类变系数线性微分方程组的零解关于部分变元是稳定的结果。
In this paper, we get the following theorem; Theorem. given a system of equations dx_s/dt=a_(s1)(t)x_1+a_(s2)(t)x_2+…+a_(sn)(t)x_n (s=1,2,…,n) (*) where aij(t) are contionuous on[t_o,+∞] and a_(ss)(t)<L(positive number); aii(t)=-aji(t) (i≠j. Again, we assume that integral from n=1 to +∞(‖A_m(t)‖dt<+∞(‖A_m(t)‖)=sum from i,j=1 to m(|a_ij(t)|~2)^(1/2)) and |a_1m+1(t)|+…+|a_1n(t)|+…+|a_(mm)+1(t)|+…+|a_(mn)(t)|<M_oe^(-α)t(α>L)M_o, α are positive numbers. Then the trivial solutions of (*) are stable to a part of variables x_1;x_2;…;x_m.
出处
《纯粹数学与应用数学》
CSCD
1989年第5期87-91,共5页
Pure and Applied Mathematics
