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分数阶微分方程边值问题非平凡解的存在性
  • ISSN号：1671-9352
  • 期刊名称：《山东大学学报：理学版》
  • 时间：0
  • 分类：O175.8[理学—数学;理学—基础数学]
  • 作者机构：[1]齐鲁师范学院数学学院,山东济南250013, [2]山东大学数学学院,山东济南250100
  • 相关基金：国家自然科学基金资助项目（10971046）; 山东省自然科学基金资助项目（ZR2012AQ007）; 山东大学自主创新基金资助项目（2012TS020）
作者： 马燕[1,2], 张克玉[2]
关键词： 分数阶边值问题, 非平凡解, Leray-Schauder度, fractional boundary value problem, nontrivial solution, Leray-Schauder degree
中文摘要：

运用Leray-Schauder度理论,在相关算子第一特征值条件下,获得分数阶微分方程边值问题{Dα0＋u（t）=-f（t,u（t））,t∈[0,1]u（0）=u＇（0）=u＇（1）=0非平凡解的存在性,其中α∈（2,3]是一实数,Dα0＋是α阶Riemann-Liouville分数阶导数。

英文摘要：

By applying the theory of Leray-Schauder degree,the existence of nontrivial solutions for the boundary value problems of fractional differential equations{Dα0 ＋ u（t）=-f（t,u（t））,t∈[0,1] u（0）=u′（0）=u′（1）=0 is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear operator.Hereα∈（2,3]is a real number,Dα0 ＋ is the standard Riemann-Liouville fractional derivative of order α.

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非线性分析及在微分方程中的应用
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期刊信息
  • 《山东大学学报：理学版》
  • 北大核心期刊（2011版）
  • 主管单位:中华人民共和国教育部
  • 主办单位:山东大学
  • 主编：刘建亚
  • 地址：济南市经十路17923号
  • 邮编：250061
  • 邮箱：xblxb@sdu.edu.cn
  • 电话：0531-88396917
  • 国际标准刊号：ISSN：1671-9352
  • 国内统一刊号：ISSN：37-1389/N
  • 邮发代号:24-222
  • 获奖情况:
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  • 被引量:6243