中文摘要：

本文在一般Banach空间中应用变分分析的手段和方法研究了具集约束的L-subsmooth多值映射具有cahnness的充分与必要条件，并得到了Asplund空间中相应的结果．在此基础上，又给出关于此类集值映射具有强calmness的充分条件、必要条件及其等价刻画．最后我们还给出一个模条件判别法．

英文摘要：

By variational analysis techniques, in this paper we study sufficient and neces- sary conditions of calmness for L-subsmooth multifunctions with constraint sets in Banach spaces, and provide sharper results in Asplund spaces, we also present the sufficient and necessary conditions of strong calmness of this kind of multifunctions. Finally, we build a modular criterion of calmness.