| 一类共振条件下分数阶多点边值问题的可解性 |
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| 引用本文： | 张宁,史小艺,张娣.一类共振条件下分数阶多点边值问题的可解性[J].五邑大学学报(自然科学版),2012,26(3):12-17,22. |
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| 作者姓名： | 张宁 史小艺 张娣 |
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| 作者单位： | 1. 中国矿业大学理学院,江苏徐州,221116
2. 中国矿业大学管理学院,江苏徐州,221116 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 利用Mawhin的连续性定理及迭合度理论,讨论了共振条件下分数阶微分方程cDβ0+α(t)cDα0+x(t)=f(t,x(t),cDβ0+α(t),cDα0+x(t)),t∈0,1] cDα0+x(0)=0,x(1)=sum from m to i=1 aix(ζi)多点边值问题解的存在性,得到解存在的充分条件,推广了整数阶微分方程共振问题已有的结果.
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| 关 键 词： | 分数阶微分方程 多点边值问题 迭合度 Mawhin连续性定理 |
Solvability of Fractional Order Muti-point Boundary Value Problems at Resonance |
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| ZHANG Ning,SHI Xiao-yi,ZHANG Di.Solvability of Fractional Order Muti-point Boundary Value Problems at Resonance[J].Journal of Wuyi University(Natural Science Edition),2012,26(3):12-17,22. |
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| Authors: | ZHANG Ning SHI Xiao-yi ZHANG Di |
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| Institution: | 1. College of Sciences, China University of Mining and Technology, Xuzhou 221116, China; 2. College of Management, China University of Mining and Technology, Xuzhou 221116, China) |
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| Abstract: | This paper discusses the existence of solutions for fractional muti-point boundary value problems at resonance cDβ0＋α（t）cDα0＋x（t）=f（t,x（t）,cDβ0＋α（t）,cDα0＋x（t））,t∈0,1] cDα0＋x（0）=0,x（1）=sum from m to i=1 aix（ζi） by using Mawhin’s continuous theorem and coincidence degree theory and the sufficient conditions for the boundary value problems is obtained,generalizing known results about integral differential equation at resonance. |
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| Keywords: | fractional differential equations muti-point boundary value problems coincidence degreetheory Mawhin's continuous theorem |
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