Banach空间常微分方程最小最大拟解对的存在性

THE COUPLED MAXIMAL AND MINIMAL QUASI-SOLUTION OF THE DIFFERENTIAL EQUATION IN BANACH SPACE

讨论了紧型条件下Ｂａｎａｃｈ空间中Ｃａｕｃｈｙ问题ｘ＇＝ｆ（ｔ，ｘ），ｘ（ｔ＿ｏ）＝ｘ＿ｏ的最小最大拟解对的存在性．推广了关于最小最大拟解对的存在定理，并给出了另外１个紧型条件下Ｂａｎａｃｈ空间中Ｃａｕｃｈｙ问题最小最大拟解对的存在定理。

The paper discusses the existence of a coupled maximal and minimal quasi-solution ofCauchy problem x'=f(t,x),x(t_o)=x_o under a compact condition in Banach space.It also extends the theoremconcerning the quasi-solution and proposes another theorem of the coupled quasi-solution under the compact condition.