分数阶微分方程边值问题非平凡解的存在性

doi:10.6040/j.issn.1671-9352.0.2014.317

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (05): 68-73.doi: 10.6040/j.issn.1671-9352.0.2014.317

分数阶微分方程边值问题非平凡解的存在性

马燕^1,2, 张克玉²

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

收稿日期:2014-07-08 出版日期:2015-05-20 发布日期:2015-05-29
作者简介:马燕(1974-),女,硕士,副教授,研究方向为泛函分析.E-mail:qlmayan@126.com
基金资助:
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)

Existence of nontrivial solutions for boundary value problems of fractional differential equations

MA Yan^1,2, ZHANG Ke-yu²

1. Department of Mathematics, Qilu Normal University, Jinan 250013, Shandong, China;
2. School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Received:2014-07-08 Online:2015-05-20 Published:2015-05-29

摘要/Abstract

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

非平凡解的存在性, 其中α∈(2,3]是一实数, D₀₊^α 是α阶Riemann-Liouville 分数阶导数。

关键词: 非平凡解, Leray-Schauder度, 分数阶边值问题

Abstract: By applying the theory of Leray-Schauder degree, the existence of nontrivial solutions for the boundary value problems of fractional differential equations

is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear operator.Here α∈(2,3]is a real number, D₀₊^α is the standard Riemann-Liouville fractional derivative of order α.

Key words: fractional boundary value problem, Leray-Schauder degree, nontrivial solution

中图分类号:

O175.8

马燕, 张克玉. 分数阶微分方程边值问题非平凡解的存在性[J]. 山东大学学报（理学版）, 2015, 50(05): 68-73.

MA Yan, ZHANG Ke-yu. Existence of nontrivial solutions for boundary value problems of fractional differential equations[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(05): 68-73.

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分数阶微分方程边值问题非平凡解的存在性

Existence of nontrivial solutions for boundary value problems of fractional differential equations

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