测度链上非一致指数型二分性的鲁棒性(英文)

Robustness of nonuniform exponential dichotomies on measure chains

研究线性非自治测度链系统在线性扰动下的一些稳定性结果。利用巴拿赫压缩映像原理和一些算子不等式,建立测度链上非一致指数型二分性的鲁棒性理论,即一个线性系统具有非一致指数型二分性,那么这个线性系统的所有邻域的线性系统具有相似的非一致指数型二分性。所有结果都是在巴拿赫空间中获得的。

Some results of stability for linear perturbations of linear nonautonomous systems on meas- ure chains are explored. With the help of the Banach contraction principle and some operator inequalities, the robustness of nonuniform exponential dichotomies on measure chains is established, that is, if a linear system admits a nonuniform exponential dichotomy, then all the neighborhood systems of this sys- tem also admit a similar nonuniform exponential dichotomy. All results are obtained in Banach spaces.