非凸情况下发展包含的反周期问题

摘要

讨论一类非凸情况下发展包含的反周期问题.当集值函数G(t,x)取紧非凸值的、关于变量t是可测的、关于变量x是下半连续时,运用连续选择定理和Schauder不动点定理,对方程作了先验估计,并给出了反周期解的存在性定理.%The authors discussed the anti-periodic problems of evolution inclusions in nonconvex case.When the mutilfuction G(t,x) takes bounded,weakly compact,nonconvex value,is measurable about variable t,and is a semi-continuous about variable x,using techniques from the continuous selection theorem and the Schauder fixed point theory,we got a priori estimate to this equation and established the existence theorem of anti-periodic solutions.