您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

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

• • 上一篇    下一篇

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

PDF (PC)

562

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
[1] OLDHAM K B, SPANIER J. The fractional calculus[M]. New York: Academic Press, 1974.
[2] KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and applications of fractional differential equations[M]. Amsterdam: Elsevier Science, 2006, 204(49-52):2453-2461.
[3] KILBAS A A, MARZAN S A. Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions[J]. Differential Equations, 2005, 41(1):84-89.
[4] METZLER R, SCHICK W, KILIAN H, et al. Relaxation in filled polymers: a fractional calculus approach[J]. Journal of Chemical Physics, 1995, 103(16):7180-7186.
[5] GOODRICH C S. On discrete sequential fractional boundary value problems[J]. Journal of Mathematical Analysis and Applications, 2012, 385(1):111-124.
[6] LAKSHMIKANTHAM V. Theory of fractional functional differential equations[J]. Nonlinear Analysis Theory Methods and Applications, 2008, 69(10):3337-3343.
[7] FENG Wenquan, SUN Shurong, HAN Zhenlai, et al. Existence of solutions for a singular system of nonlinear fractional differential equations[J]. Computers and Mathematics with Applications, 2011, 62(3):1370-1378.
[8] FENG Haixing, ZHAI Chengbo. Existence and uniqueness of positive solutions for a class of fractional differential equation with integral boundary conditions[J]. Nonlinear Analysis Modelling and Control, 2017, 22(2):160-172.
[9] WANG Lin, LU Xinyi. Existence and uniqueness of solutions for a singular system of highter-order nonlinear fractional differential equations with integral boundary conditions[J]. Nonlinear Analysis: Modelling and Control, 2013, 31(31):493-518.
[10] LIANG Sihua, ZHANG Jihui. The existence of three positive solutions for some nonlinear boundary value problems on the half-line[J]. Positivity, 2009, 13(2):443-457.
[11] FERREIRA RAC. Positive solutions for a class of boundary value problems with fractional q-differences[J]. Pergamon Press, Inc, 2011, 61(2):367-373.
[12] YUAN Chengjun. Two positive solutions for(n-1,1)-type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations[J]. Communications in Nonlinear Science and Numerical Simulation, 2012, 17(2):930-942.
[13] YANG Chen, ZHAI Chengbo. Uniqueness of positive solutions for a fractional differential equation via a fixed point theorem of a sum operator[J]. Electronic Journal of Differential Equations, 2012, 2012(70):808-826.
[14] ZHAI Chengbo, YAN Weiping, YANG Chen. A sum operator method for the existence and uniqueness of positive solutions to Riemann-Liouville fractional differential equation boundary value problems[J]. Communications in Nonlinear Science and Numerical Simulation, 2013, 18(4):858-866.
[15] 郭大钧. 非线性分析中的半序方法[M].济南:山东科学技术出版社,2000. GUO Dajun. Partial methods in nonlinear analysis[M]. Jinan: Shandong Science and Technology Press, 2000.
[1] 王娇. 一类非线性二阶常微分方程 Dirichlet问题正解的存在性[J]. 山东大学学报（理学版）, 2018, 53(6): 64-69.
[2] 闫东亮. 带有导数项的二阶周期问题正解[J]. 山东大学学报（理学版）, 2017, 52(9): 69-75.
[3] 李涛涛. 二阶半正椭圆微分方程径向正解的存在性[J]. 山东大学学报（理学版）, 2017, 52(4): 48-55.
[4] 郭丽君. 非线性微分方程三阶三点边值问题正解的存在性[J]. 山东大学学报（理学版）, 2016, 51(12): 47-53.
[5] 杨文彬, 李艳玲. 一类具有非单调生长率的捕食-食饵系统的动力学[J]. 山东大学学报（理学版）, 2015, 50(03): 80-87.
[6] 孙艳梅. 奇异分数阶微分方程边值问题正解的存在性[J]. 山东大学学报（理学版）, 2014, 49(2): 71-75.
[7] 张露,马如云. 渐近线性二阶半正离散边值问题正解的分歧结构[J]. 山东大学学报（理学版）, 2014, 49(03): 79-83.
[8] 秦小娜,贾梅*,刘帅. 具Caputo导数分数阶微分方程边值问题正解的存在性[J]. J4, 2013, 48(10): 62-67.
[9] 姚庆六. 奇异非自治三阶两点边值问题的正解存在性[J]. J4, 2012, 47(6): 10-15.
[10] 范进军,张雪玲,刘衍胜. 时间测度上带p-Laplace算子的m点边值问题正解的存在性[J]. J4, 2012, 47(6): 16-19.
[11] 卢芳,周宗福*. 一类具p-Laplacian算子四阶奇异边值问题正解的存在性[J]. J4, 2012, 47(6): 28-33.
[12] 张海燕1,2,李耀红2. 非线性混合高阶奇异微分方程组边值问题的正解[J]. J4, 2012, 47(2): 31-35.
[13] 郑春华. 具有时滞的二阶微分方程三点边值问题三个正解的存在性[J]. J4, 2012, 47(12): 109-114.
[14] 刘树宽. 二阶m点边值问题的三个正解[J]. J4, 2012, 47(10): 38-44.
[15] 杨春风. 一类三阶三点边值问题正解的存在性和不存在性[J]. J4, 2012, 47(10): 109-115.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发