Banach流形上一类非线性方程的解集的结构  

A STRUCTURE TO THE SOLUTION SET OF A NONLINEAR EQUATION ON BANACH MANIFOLDS

作　　者：史平[1] 马吉溥[2] 

机构地区：[1]南京财经大学应用数学系,南京210003 [2]南京大学数学系,南京210093

出　　处：《数学年刊（A辑）》2004年第6期745-752,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10271053)教育部博士点基金资助的项目.

摘　　要：设f是两个Ck(k≥1)Banach流形M和Ⅳ之间的C1映射.由f定义M上的一个三重指标(M(x),Mc(x),Mr(x)),用此三重指标刻画了f的局部精细点.同时当y是f的广义正则值时,获得原像f-1(y)中含x0的连通分支是M中一个具有维数为M(x0)的C1Banach子流形.特别地,给出非线性方程f(x)=y的孤立解的一个特征.Let / be a C1 mapping between two Ck (k≥1) Banach manifolds M and N. We define a triple index (M(x),Mc(x), Mr(x)) on M by f, from which the locally fine points of f are characterized. Moreover, when y is a generalized regular value of f, the authors obtain that the connected component containing x0 of the preimage f-1(y) is a C1 Banach submanifold of M with dimension M(x0). In particular, a characterization of isolated solutions of a nonlinear equation f(x) = y is given.

关 键 词：广义正则值 指标 Banach子流形 切空间 维数 

分 类 号：O177.91[理学—数学]