关于Banach空间中一类非线性方程的若干问题  

Some Problems On a Class of Nonlinear Eqliations in Banach Space

作　　者：杨书郎[1] 

机构地区：[1]厦门大学系统科学系

出　　处：《数学学报（中文版）》1995年第3期371-380,共10页Acta Mathematica Sinica：Chinese Series

摘　　要：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。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.

关 键 词：巴拿赫空间 非线性 微分方程 两点边值问题 

分 类 号：O175.15[理学—数学]