一类具有非线性边值条件的非线性分数阶微分方程正解的存在性（英文）  

Existence of Positive Solutions for a Kind of Nonlinear Fractional Differential Equation with Nonlinear Boundary Value Conditions

作　　者：李梦婷 张克梅[1] LI Mengting;ZHANG Kemei(School of Mathematical Sciences,Qufu Normal University,Qufu 273165,China)

机构地区：[1]曲阜师范大学数学科学学院

出　　处：《应用数学》2020年第1期126-137,共12页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11571197);the Natural Science Foundation of Shandong Province of China(ZR2016FM10)

摘　　要：本文研究一类非线性分数阶边值问题正解的存在唯一性问题.利用混合单调算子的方法,获得至少一个正解的存在性结果,推广了整数阶边值问题的存在唯一性结果.In this paper,we use mixed monotone operator method to deal with the existence and uniqueness of positive solutions to a kind of boundary value problem of the nonlinear fractional order differential equation.Our analysis is based on one new fixed point theorem for the mixed monotone operator.As an application,we also give a simple example to prove our main conclusions.

关 键 词：正解 混合单调算子 Riemann-Liouville分数阶导数 存在唯一性 

分 类 号：O175.8[理学—数学]