有序Banach空间上非线性分数阶边值问题的解  

Solution of nonlinear fractional boundary value problem on ordered Banach space

作　　者：胡行华[1] 孙文婷 Hu Xinghua;Sun Wenting(Institute of Optimization and Decision,Liaoning Technical University,Fuxin 123000,China)

机构地区：[1]辽宁工程技术大学优化与决策研究所,辽宁阜新123000

出　　处：《南京理工大学学报》2021年第6期738-742,共5页Journal of Nanjing University of Science and Technology

基　　金：国家自然科学基金(51704140);辽宁省教育厅高等学校基本科研项目(LJYL043,LJ2019-1151)。

摘　　要：该文研究在有序Banach空间中同时具有Riemann-Liouville微分和非线性项含有未知函数导数的非线性分数阶微分方程边值问题。由非线性微分方程所对应的线性微分方程,得到1个在有序Banach空间上的凝聚映射,再根据凝聚映射上的Leray-Schauder不动点定理获得非线性边值问题解的存在性理论。The boundary value problem is studied for nonlinear fractional differential equation with Riemann-Liouville differential and nonlinear term with unknown function derivative in ordered Banach space.From the linear differential equation corresponding to the nonlinear differential equation,a condensing mapping on the ordered Banach space is obtained,and then the existence theory of the solution of the nonlinear boundary value problem is obtained according to the Leray-Schauder fixed point theorem on the condensing mapping.

关 键 词：有序BANACH空间 分数阶微分 凝聚映射 LERAY-SCHAUDER不动点定理 非线性边值 

分 类 号：O175.6[理学—数学] O175.8[理学—基础数学]