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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2016, Vol. 31 Issue (2): 167-175    DOI:
    
Existence of multiple positive solutions for a boundary value problem of fractional difference equation
WANG Jin-hua, XIANG Hong-jun
College of Mathematics and Finance, Xiangnan University, Chenzhou 423000, China
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Abstract  By constructing the corresponding Green’s function and analysing the key properties with inequality technique, a high order fractional difference equation with boundary value conditions is studied in this paper. The existence of multiple positive solutions is obtained by using the fixed point index theory. Additionally, two examples are illustrated to guarantee the main results.

Key words： multiple positive solution      boundary value problem      fractional difference equation      existence     
Received: 21 November 2015      Published: 17 May 2018
CLC:  O175.7  
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WANG Jin-hua
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Cite this article:

WANG Jin-hua, XIANG Hong-jun. Existence of multiple positive solutions for a boundary value problem of fractional difference equation. Applied Mathematics A Journal of Chinese Universities, 2016, 31(2): 167-175.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2016/V31/I2/167


一类分数阶差分方程边值问题多重正解的存在性

考虑一类高阶分数阶差分方程边值问题. 构造相关的格林函数, 利用不等式技巧, 分析格林函数的特征性质. 运用不动点指数理论, 获得了该分数阶差分方程边值问题存在多重正解的充分条件, 举例说明了所获理论的有效性.

关键词： 多重正解,  边值问题,  分数阶差分方程,  存在性 
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