关于Banach空间中一类非线性方程的若干问题

本文引入边界条件（Ｓｗ，Ａ，ａ）与（ＬＭ，ｗ），建立有关ｋ－集压缩局部固有场的延拓与不动点指数计算的一些结果；结合弱半可微性，研究一类非线性方程的正解、多正解和固有元集等问题，作为一个应用，还研究了两点边值问题。

Some Problems On a Class of Nonlinear Eqliations in Banach Space

In the paper,the boundary conditions(Sω,A,a)and(LM,ω)are introduced,the resultson the extension and the computation of fixed point index for k-set-contraction locally properfield are established.Use them with the weak semidifferentiability, the problems concerningthe positive solution,the multiple positive solutions and the set of eigenvectors for a class ofnonlinear equations are studied.And as an application, a two point boundary value problem isstudied in this paper.