两点拉伸型不动点定理及其应用

FIXED POINT THEOREMS OF TWO-POINT EXTENSION TYPE AND APPLICATIONS

在研究各种非线性方程解的存在性问题时,上下解方法是一个强有力的工具.设 E是 Banach 空间,P 是 E 中的锥,E 中的半序由 P 导出.设 A:E→E 是一个算子.如果x_0∈E

Let E be a Banach space,P a cone in E,and A∶P→P an increasing opera-tor.If there exist x_0,y_0∈P such that X_0≤Ax_0,Ay_0≤y_0 and x_0(?)y_0,then A issaid to the two-point extension condition.Some fixed point theorems are provedunder the two-point extension condition,and some applications to the nonlinearSturm-Liouville problem are given.