Banach空间中的积分算子不动点定理及其应用

Multiple Postive Solutions of Nonlinear Multi-Point Boundary Value Problem in Banach Spaces

利用不动点指数理论得到了若干个积分算子的不动点定理,这些结论可用于研究许多边值问题.利用这些结论研究了Banach空间中二阶两点边值问题正解的存在性,特别的,在有些情况下去掉了Banach空间中的锥必须是正规的这一条件限制,而这一条件限制在许多文献中是必须的.

Some fixed point theorems of integral operator are given firstly by using fixed point index theory. These results can be used to solve many problems. In this paper, applying these results, we study the existence of positive solutions for two-point boundary value problems in Banach spaces. Particularly, sometimes, we don＇t need that the cone in Banach space is normal, which is essential for the technique used in many papers.