非线性无穷维中立型大系统的解在C_1空间中的稳定性

Stability of Solutions for the Infinite Dimensional Nonlinear System of NFDE in Banach Space

文章讨论了具变时滞的非线性无穷维中立型大系统x_j'(t)=A_j(t)x_j(t)+sum from t=■to ∞A_(tj)(t)x_j(t)+F_t(t, x(t-τ(t)),x'(t-τ(t))) (i=1,2,…,∞)的零解在Banach空间中的稳定性。借助于矩阵测度,得到了若干解的稳定性和渐近稳定性判据。

This paper is devoted to a discussion of the stability of zero solutions for the infinite dimensional nonlinear system of NFDE (neutral functional differential equations) with varying time delay x_1(t)=A_1(t)x_1(t)+(?)(t)x_1(t)+F_1(t, x(t—((?)t)), x'(t-t(t))) (i-1, 2, '', ∞) By means of measure of matrix and inequality method, some criteria for zero solutions of the above equation to be stabile and asymptotically stabile are obtained.