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

Boundary Value Problems

Hui Wang¹  Lingling Zhang¹  Xiaoqiang Wang² 

[1] College of Mathematics, Taiyuan University of Technology;Department of Scientific Computing, Florida State University;

关键词: Sum-type operator;    Existence and uniqueness;    Positive solution;    Fractional differential equation;    Fractional boundary condition;   

DOI  :  10.1186/s13661-018-1059-y

来源: DOAJ

【 摘 要 】

Abstract In this paper, we consider the fixed point for a class of nonlinear sum-type operators ‘ A+B+C $A+B+C$’ 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.

【 授权许可】

Unknown