中文摘要：

考虑一类发展包含在Banach空间中的反周期问题,集值函数G（t,x）取有界紧凸值的,关于变量t是可测的,关于变量x是闭图像,运用Kakutani-Fan不动点定理,对方程做了先验估计,给出了解存在的充分条件,并证明了解集是弱紧的.

英文摘要：

The authors discussed the anti-periodic problems for a class of evolution inclusions in Banach space.When the mutilfuction G（t,x） takes a bounded,weakly compact,convex value,and is measurable about variable t,is a closed graph about variable x,using techniques from the Kakutani-Fan fixed point theory,we have got a priori estimate to this equation and a sufficient condition of the existence of solutions,and proved the solution set is weakly compact.