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

张宁1，史小艺1，张娣2

（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)

分数阶微分方程；多点边值问题；迭合度；Mawhin连续性定理

近年，关于分数阶微分方程边值问题的理论研究取得了不少成果[1-12]，共振条件下分数阶微分方程多点边值问题作为分数阶非局部边值问题的一种特殊情况，也受到了研究者们的重视，越来越多的人运用Mawhin的连续性定理来研究多点边值问题，如文献[6]研究了共振条件如下的分数阶微分方程的多点边值问题：

受此启发，本文研究共振条件如下的序列分数阶微分方程多点边值问题：

1 预备知识

首先介绍一些关于迭合度的基本理论.

2 几个有用的引理

和

因此，

结合引理2，得到下面的引理.

3 解的存在性定理

或者

所以

由式（8），有

通过以上讨论易知满足定理1的条件1）和2），下证定理1的条件3）也是满足的.

.

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Solvability of Fractional Order Muti-point Boundary Value Problems at Resonance

ZHANGNing1, SHIXiao-yi1, ZHANGDi2

(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)

fractional differential equations; muti-point boundary value problems; coincidence degree theory; Mawhin’s continuous theorem

1006-7302（2012）03-0012-06

O175.8

A

2012-03-16

国家自然科学基金资助项目（10771212）

张宁（1985—），女，山西晋城人，在读硕士生，研究方向为微分方程边值问题.