摘要
本文考虑下面形式的微分方程 =A(t,x)x + g(t,x), (1)这里x∈R^n,A(t,x)是定义在R×R^n上的n×n连续矩阵,g(t,x):R×R^n→R^n关于t,x连续.本文主要讨论方程(1)的概周期解存在性,所得结果推广了以前一些已知结果.
In this paper, using Rothe fixed point theorem and exponential dichotomy, we establish the main results as follows.Theorem Suppose there exists a regular bounded Hermitian matrix P(t) such that the eigenvalues λi(t,x) (i = 1,2,…,n) of matrixM(t,x) = P(t)(t,x) + A (t,x)P(t) + P(t), satisfying λj(t,x) ≤- δ < 0 for t ∈ R, |x| ≤ R0.IFthen almost periodic differential equationx = A(t,x)x + g(t,x)has at least an almost periodic solution x(t) with mod (x) mod (A,g) . Applying above theorem to Abel differential equation, we obtain some new results on existence of almost periodic solutions.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
1992年第4期610-614,共5页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
