河北师范大学学报—

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刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
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分数阶共振向量边值问题解的存在性

（河北科技大学理学院，河北石家庄 050018）
DOI： 10.13763/j.cnki.jhebnu.nse.202401006

Existence of Solutions for Fractional Order Vector Boundary Value Problems at Resonance

SI Huanmin，JIANG Weihua，WANG Luyao

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摘要/Abstract

摘要：

研究了一类带有系数矩阵的分数阶共振边值问题.首先，定义2个合适的Banach空间；然后，在Banach空间中构造恰当的算子并使用仿伪逆矩阵的性质及Mawhin的重合度理论，得到了其解的存在性；最后，给出一个例子来验证主要结果.

Abstract：

This paper studies the fractional boundary value problems(BVPs) with a matrix of coefficients at resonance.First，we construct two suitable Banach spaces.Then，the existence of fractional vector BVPs is obtained by defining an appropriate operator in Banach space using the properties of pseudo-inverse matrices and Mawhin′s coincidence degree theory.Finally，we give examples to illustrate the main results.

关键词

关键词： 常微分方程；向量边值问题；仿伪逆矩阵； Mawhin的重合度理论；共振

Key words： ordinary differential equation ; vector boundary value problem ; pseudo-inverse matrix ; Mawhin′s coincidence degree theory ; resonance

参考文献 13

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