混合单调算子的两点拉伸型不动点定理  

Two-Point Expansion Fixed Point Theorems of Mixed Monotone Operators

作　　者：刘进生[1] 李福义[2] 

机构地区：[1]太原理工大学数学系,太原030024 [2]山西大学数学系,太原030006

出　　处：《数学学报（中文版）》2003年第6期1117-1122,共6页Acta Mathematica Sinica：Chinese Series

基　　金：山西省青年科技基金资助项目(20021001)

摘　　要：本文首次提出了混合单调算子不动点的两点拉伸型条件.同时,利用锥映象的不动点指数理论建立了一类特殊的两点拉伸型混合单调算子的不动点存在性定理,并将所得结论应用于带有超线性项的积分方程与微分方程上,得到了新的结论.因而在本质上推进了混合单调算子不动点问题的研究.In this paper, the two-point expansion condition of fixed point for the mixed monotone operator is first given, and some existence theorems for fixed point for a special class of two-point expansion mixed monotone operators are established by using the fixed point index theory for operators from a cone to itself. The results obtained here are applied to Hammerstein integral equations and two-point boundary value problems for a fourth order differential equation and therefore some new conclusions are obtained.

关 键 词：混合单调算子 两点拉伸型条件 锥 不动点指数理论 

分 类 号：O177.91[理学—数学]