Banach空间含间断项微分方程的广义解

Generalized solutions of differential equations with discontinuous terms in Banach spaces

通过上下解的单调迭代方法 ,获得了有序Banach空间E中常微分方程初值问题u′ =f(t,u) ,u( 0 ) =x0 解的存在唯一性结果 .这里不要求f:I×EE连续 。

The results of existence and uniqueness of solutions for differential equation initial value problem u′=f(t,u),u(0)=x 0 in ordered Banach spaces are obtained by using the monotone iterative method with upper and lower solutions.Where f:I×EE ,which does not require to be continuous,only satisfies the condition of mapping continuous functions into strongly measurabe functions.