AAH不动点定理与二阶非线性方程的正解  

AAH fixed point theorem and positive solution to nonlinear equation of second order

作　　者：徐厚生[1] 王波 XU Housheng;WANG Bo(School of Science,Shenyang Jianzhu University,Shenyang 110168,China;Department of Mathematics,Northeastern University,Shenyang 110819,China)

机构地区：[1]沈阳建筑大学理学院,沈阳110168 [2]东北大学理学院,沈阳110819

出　　处：《沈阳师范大学学报（自然科学版）》2018年第4期311-317,共7页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11701390);辽宁省科技厅自然科学基金资助项目(20170540769)

摘　　要：泛函形式的锥拉伸与压缩型不动点定理已有多种不同的结果,其本质上是范数形式锥拉伸与压缩型不动点定理的推广。这些定理在研究方程正解问题时具有广泛应用,不同的定理中不同的泛函约束条件使得在实际使用时可以根据具体的方程,特别是方程中的非线性函数进行灵活选择。应用建立在锥理论和不动点指数方法基础上的Anderson-Avery-Henderson不动点定理(简称为AAH不动点定理)。研究一类与文献中不同类型的二阶非线性边值问题正解的存在性。当非线性项满足单调性和某些不等式条件时,给出该类二阶非线性边值问题正解存在的锥拉伸与压缩型充分条件,并且通过一些例子来说明结论的应用.There are many different results on the cone expansion and compression fixed point theorems with functional forms,and they are essentially the extension of the cone expansion and compression fixed point theorems with norm form.These theorems are widely applied to the study of positive solutions of equations,different functional constraints in different theorems can be flexibly chosen according to the specific equations,especially the nonlinear functions in the equation.By using of Anderson-Avery-Henderson fixed point theorem（or AAH theorem for short）based on the cone theory and fixed point index methods,we investigate the existence of positive solutions to nonlinear boundary value problem of second order the type of which is different from those in the references.Some sufficient conditions about cone expansion and compression are provided to guarantee the existence of positive solution to the equation when the nonlinear term satisfies monotonicity condition and some inequalities.Some examples are given to illustrate the applications of the conclusions.

关 键 词：正解 不动点 锥 凸泛函 凹泛函 

分 类 号：O175.14[理学—数学]