关于Banach空间中可微映象的一个注记

E是赋范空间 ,Y是Banach空间 ,g∶Ω E→Y是Fr啨ｃｈｅｔ可微映象 ,这里Ω是开的 ,作者得出 :对任意给定的v ∈Y ,y∈X ,存在u ∈Y ,使得 g(x0 +h(y +Lu) ) =g(x0 ) +hg′(x0 ) (y+Lu) ]+h(v -h) ,这里L∶Y →X线性连续 ;这一结论在研究二阶微分方程不变流问题中起着重要作用 .

A note on differentiable mappings in Banach spaces

Let E be a normed space, g∶ΩE→Y a Fréchet differentiable mapping, where Ω is open and Y is a Banach space. Given v∈Y,y∈X, the author studied the existence of u∈Y, such continuous; such a problem plays a key role in studying the flow invariance of second order differential equation.