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山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (12): 48-57.doi: 10.6040/j.issn.1671-9352.0.2017.380

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高阶非线性分数阶微分方程系统的多个正解

冯海星1,翟成波2*   

  1. 1.山西财经大学应用数学学院, 山西 太原 030031;2.山西大学数学科学学院, 山西 太原 030006
  • 收稿日期:2017-07-31 出版日期:2017-12-20 发布日期:2017-12-22
  • 通讯作者: 翟成波(1977— ),男,博士,教授,研究方向为非线性泛函微分方程. E-mail:cbzhai@sxu.edu.cn E-mail:seastar1981@126.com
  • 作者简介:冯海星(1981— ),女,硕士,讲师,研究方向为非线性泛函微分方程. E-mail:seastar1981@126.com
  • 基金资助:
    国家自然科学基金青年科学基金资助项目(11201272);山西省自然科学基金资助项目(2015011005);2015山西省131人才项目;山西财经大学青年基金资助项目(2014026)

Multiple positive solutions of a system of high order nonlinear fractional differential equations

FENG Hai-xing1, ZHAI Cheng-bo2*   

  1. 1. College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030031, Shanxi, China;
    2. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China
  • Received:2017-07-31 Online:2017-12-20 Published:2017-12-22

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摘要： 研究了一类具有积分边值条件的高阶非线性分数阶微分方程系统多个正解的存在性,主要运用Leggett-Williams不动点定理及Krasnoselskii锥上的不动点相关定理得出了该系统存在两个或三个正解的结果。

关键词: 分数阶微分方程系统, Leggett-Williams不动点定理, 积分边值条件, 正解

Abstract: The existence of multiple positive solutions for a system of high-order nonlinear fractional differential equations is studied. Two or three positive solutions are obtained for the system by using Leggett-Williams fixed point theorem and Krasnoselskiion cone.

Key words: integral boundary value conditions, positive solution, Leggett-Williams fixed point theorem, the system of fractional order differential equation

中图分类号: 

  • O177.91
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