刘锡平,贾梅,牛铭,相秀芬.分数阶微分方程多点边值问题的正解[J].数学研究及应用,2017,37(2):223~232
分数阶微分方程多点边值问题的正解
Multiple Positive Solutions for Multi-Point Boundary Value Problem of Fractional Differential Equation
投稿时间:2016-04-25  最后修改时间:2016-11-02
DOI:10.3770/j.issn:2095-2651.2017.02.011
中文关键词:  分数阶微分方程  多点边值问题  正解  Green函数  不动点定理
英文关键词:fractional differential equation  multi-point boundary value problem  positive solution  Green function  fixed point theorem
基金项目:国家自然科学基金(Grant No.11171220),沪江基金(Grant No.B14005).
作者单位
刘锡平 上海理工大学理学院, 上海 200093 
贾梅 上海理工大学理学院, 上海 200093 
牛铭 石家庄职业技术学院机电工程系, 河北 石家庄 050081 
相秀芬 承德石油高等专科学校社科与数理部, 河北 承德 067000 
摘要点击次数: 528
全文下载次数: 579
中文摘要:
      本文研究了在边界条件中含有多个分数导数项的分数阶微分方程多点边值问题多个正解的存在性.运用Green函数的性质以及有白-葛推导出的一般形式的Leggett-Williams不动点定理,建立了边值问题至少有三个正解存在的充分条件.最后,给出了一个例子,用于说明所得主要结论具有广泛的适用性.
英文摘要:
      In this paper, we study the multiplicity of positive solutions for multi-point boundary value problem of Riemann-Liouville fractional differential equation with multi-terms fractional derivative in the boundary conditions. By using the properties of the Green function and a generalization of the Leggett-Williams fixed point theorem due to the work of Bai and Ge, the sufficient conditions to guarantee the existence of at least three positive solutions are established. In the end of this paper, we have also given out the example to illustrate the wide range of potential application of our main results.
查看全文  查看/发表评论  下载PDF阅读器