本文利用泛函分析的方法,借助于Schauder的不动点定理和矩阵测度的性质,对系统(1.1)的周期解的存在性进行了讨论.给出一个可以直接从系统(1.1)的右端函数性质来判别其周期解存在的定理.
Abstract
In this paper, the periodic system
x=A(t,x)+b(t,x)
is considered, where the n×n matrix A(t,x) and the,n-vector b(t,x) are continuous in(t,x)∈R×Rn,and A(t+ω,x)=A(t,x);b(t+ω,x)=b(t,x), Using the method of functional analysis, we prove that the above system has ω-periodic solution and give sufficient conditions to guarantee the existence of the unique ω-periodic solution for the following systems.
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参考文献
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