集值映射的连续不动点定理及其在微分包含中的应用

The Continuous Fixed Poin Theorem for a Set Valued Function and Its Application to a Differential Inclusion

本文首先证明了一类集值映射的下半连续性 .在此基础上给出了 Banach空间集值映射的一个连续不动点定理 ,作为应用 ,证明了一类微分包含解的存在性 .

In this paper,weshow the low semi-continuity fora kind of setvalued functions. Sequentially, we give a continuous fixed point theorem for a setvalued function on the Banach space.As its application, we prove an existence theorem fora parameterized differential inclusion,meanwhile,pointoutthe continuity of the solutions with respectto the parameter. This method is new completely.