摘要
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.
出处
《南昌航空工业学院学报》
CAS
1992年第2期40-48,共9页
Journal of Nanchang Institute of Aeronautical Technology(Natural Science Edition)
基金
江西省自然科学基金~~
关键词
微分方程
初值问题
BANACH空间
Banach space
Differential equition
Initial value problem
Solvability
The condition of the weakly compact type