Fixed point theorems for a class of nonlinear sum-type operators and application in a fractional differential equation

被引：4

作者：

Wang, Hui ^{[1
]}

Zhang, Lingling ^{[1
]}

Wang, Xiaoqiang ^{[2
]}

机构：

[1] Taiyuan Univ Technol, Coll Math, Taiyuan, Shanxi, Peoples R China

[2] Florida State Univ, Dept Sci Comp, Tallahassee, FL 32306 USA

来源：

BOUNDARY VALUE PROBLEMS | 2018年

关键词：

Sum-type operator; Existence and uniqueness; Positive solution; Fractional differential equation; Fractional boundary condition; MIXED MONOTONE-OPERATORS; POSITIVE SOLUTIONS; EXISTENCE; UNIQUENESS; CONVEX;

D O I：

10.1186/s13661-018-1059-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the fixed point for a class of nonlinear sum-type operators 'A +B+ C' on an ordered Banach space, where A, B are two mixed monotone operators, C is an increasing operator. Without assuming the existence of upper-lower solutions or compactness or continuity conditions, we prove the unique existence of a positive fixed point and also construct two iterative schemes to approximate it. As applications, we research a nonlinear fractional differential equation with multi-point fractional boundary conditions. By using the obtained fixed point theorems of sum-type operator, we get the sufficient conditions which guarantee the existence and uniqueness of positive solutions. At last, a specific example is provided to illustrate our result.

引用

页数：21

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