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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2014, Vol. 29 Issue (4): 443-452    DOI:
    
Positive solutions for boundary value problem of fractional differential equation with $p$-Laplacian operator
SONG Li-mei
School of Mathematics, Jiaying University, Meizhou 514015, China
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Abstract  The boundary value problem of fractional functional differential equations with $p$-Laplacian operator are studied. Using the fixed point theorem on cones, sufficient conditions are given for the existence of single and multiple positive solutions. The results generalize some previous results. Several examples are given to illustrate the results.

Key words： fractional functional differential equation      $p$-Laplacian operator      boundary value problem      fixed point theorem      positive solution     
Received: 22 April 2014      Published: 08 June 2018
CLC:  O175.8  
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SONG Li-mei
Cite this article:

SONG Li-mei. Positive solutions for boundary value problem of fractional differential equation with $p$-Laplacian operator. Applied Mathematics A Journal of Chinese Universities, 2014, 29(4): 443-452.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2014/V29/I4/443


具$p$-Laplace算子的分数阶微分方程边值问题的正解

考虑具有$p$-Laplace 算子的分数阶泛函微分方程边值问题，利用锥上的不动点定理, 得到了其正解及多个正解存在的充分条件, 所得结果推广了已有的结论, 并举例说明了结论的适用性.

关键词： 分数阶泛函微分方程,  $p$-Laplace 算子,  边值问题,  不动点定理,  正解 
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