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山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (6): 78-84.doi: 10.6040/j.issn.1671-9352.0.2015.632

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含参数及p-Laplacian算子的奇异分数阶微分方程积分边值问题的正解

仲秋艳1,张兴秋2,3   

  1. 1.济宁医学院信息技术中心, 山东 济宁 272067;2.济宁医学院医学信息工程学院, 山东 日照 276826;3.聊城大学数学科学学院, 山东 聊城 252059
  • 收稿日期:2015-12-29 出版日期:2016-06-20 发布日期:2016-06-15
  • 作者简介:仲秋艳(1973— ),女,硕士,实验师,研究方向为微分方程理论及应用. E-mail:zhqy197308@163.com
  • 基金资助:
    济宁医学院科技计划(JY2015KJ019,JYQ14KJ06,JY2015BS07);国家自然科学基金资助项目(11371221,11571197,11571296);山东省自然科学基金(ZR2015AL002);山东省高校科技发展计划(J15LI16)

Positive solutions for some singular fractional differential equation integral boundary value problems with p-Laplacian and a parameter

ZHONG Qiu-yan1, ZHANG Xing-qiu2,3   

  1. 1. Department of Information Technology, Jining Medical College, Jining 272067, Shandong, China;
    2. School of Medical Information Engineering, Jining Medical College, Rizhao 276826, Shandong, China;
    3. School of Mathematics, Liaocheng University, Liaocheng 252059, Shandong, China
  • Received:2015-12-29 Online:2016-06-20 Published:2016-06-15

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摘要： 利用Green函数的性质构造出合适的锥,引入适当的高度函数并考虑高度函数在锥中某些有界集合上的积分,研究一类具有p-Laplacian算子的非线性奇异分数阶微分方程积分边值问题的局部正解以及多个局部正解。非线性项f允许关于时间和空间变量具有奇异性。

关键词: 奇异性, p-Laplacian算子, 分数阶微分方程, 高度函数

Abstract: A special cone is constructed by means of the properties of Green function. By introducing height functions of the nonlinear term on some bounded sets and considering integrations of these height functions, several existence and multiplicity of local positive solutions theorems for some nonlinear fractional differential equation integral boundary value problems with p-Laplacian and a parameter are obtained. The nonlinear term f permits singularities with respect to both the time and space variables.

Key words: fractional differential equation, singularity, p-Laplacian, height functions

中图分类号: 

  • O175.8
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