弱紧型条件下Banach空间中微分方程的解

Solutions of differential equations in a Banach Space under the condition of weakly compact type

本文在弱紧型条件下讨论了Banach空间中常微分方程初值问题(1):u′=f(t,u),u(0)=u_0的可解性。首先,采用上、下解方法,较之文[1]使用的紧型条件较弱,并且比文[2]适用的弱序列完备的Banach空间更广,得到了定理1;然后,对f(t,u)可分解为式(19)的情形,采用上、下拟解方法,比文[3]的紧型条件较弱,得到了定理2。

In this paper,the solvability theorems of the initial value problem(IVP)for the ordinary differential equation in a Banach space u'=f(t,u),u(0)=u_0 have been discussed by the method of upper and lower solutions as well as the method of upper and lower quasi — solutions under the condition of the weakly compact type.