三阶泛函微分方程的周期解

利用Brouwer度理论得到了泛函微分方程x′″（t） ∑i=0^2[αix(i)(t) bix(i)(t-τi)] g1(x(t)) g2(x(t-τ））=p（t）存在2π周期解的充分性条件，推广了[1]中的有关结果．     

SOME KINDS OF LIAPUNOV FUNCTIONAL IN STABILITY THEORY OF RFDE

ＳＯＭＥＫＩＮＤＳＯＦＬＩＡＰＵＮＯＶＦＵＮＣＴＩＯＮＡＬＩＮＳＴＡＢＩＬＩＴＹＴＨＥＯＲＹＯＦＲＦＤＥＤＵＸＵＥＴＡＮＧ（杜雪堂）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｓｈａ４１００...     

On the decomposition problem of stability for Volterra integrodifferential equations

In this paper, we discuss the problem of stability of Volterra integrodifferential equationwith the decompositionwhere andin which is an matrix of functionB continuous forin which is an matrix of functionscontinuous for 0≤S≤ t<∞.According to the decomposition theory of large scale system and with the help of Liapunovfunctional, we give a criterion for concluding that the zero solution of (2) (i.e. large scale system(1)) is uniformly asymptotically stable.We also discuss the large scale system with the decompositionand give a criterion for determining that the solutions of (4) (i.e. large scale system (3)) areuniformly bounded and uniformly ultimately bounded.Those criteria are of simple forms, easily checked and applied.     

Volterra积分微分方程解的稳定性与有界性

这里A为n×n常数矩阵,C(t,s)为n×n函数矩阵,对0≤s≤t<∞连续,f:(-∞,∞)→R~n连续。 我们规定‖·‖表示向量x=(x_1,x_2,…,x_s)~T或矩阵A=(aij)_(s×s)的模,T表示转置。我们取     

Volterra积分微分方程关于部分变元的稳定性

本文给出了 Volterra 积分微分方程的零解关于部分变元的稳定性定义,并建立了几个判定定理。