Banach空间微分方程广义弱解的整体存在性

Global Existence of Generalized Weak Solutions for Differential Equations in a Banach Space

在弱完备的实Banach空间E中考虑微分方程的Cauchy问题:x′(t)=f(t,x(t)),x(0)=x0,其中x0∈E,f:J×E→E(J=[0,+∞))。通过使用弱非紧型条件给出(Cauchy problem,Cp)的广义弱解的整体存在性。

The Cauchy problem is considered for differential equations in a weakly complete Banach Space E： x＇（t）=f（t,x（t））,x（0）=x0, （Cp） where x0∈E,f：J×B→E（J=[0,a], D belong bo E）. By using weak noncompact type＇s conditions, a global existence theorem of generalized weak solutions to equa. （Cp） is obtained.