具Caputo导数分数阶微分方程边值问题正解的存在性

J4 ›› 2013, Vol. 48 ›› Issue (10): 62-67.

具Caputo导数分数阶微分方程边值问题正解的存在性

秦小娜,贾梅*,刘帅

上海理工大学理学院,上海 200093

收稿日期:2013-03-01 发布日期:2013-10-14
通讯作者: 贾梅(1963- ), 女, 副教授, 从事常微分方程理论及应用研究.Email:jiameiusst@163.com
作者简介:秦小娜(1987-) , 女, 硕士研究生, 研究方向为应用常微分方程. Email:xiaonaqin@126.com
基金资助:
国家自然科学基金资助(11171220); 上海市教委科研创新基金重点资助项目(10ZZ93)

Existence of positive solutions for fractional differential equations boundary value problems with Caputo derivative

QIN Xiao-na, JIA Mei*, LIU Shuai

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received:2013-03-01 Published:2013-10-14

摘要/Abstract

摘要：

研究了一类具有Caputo导数的分数阶微分方程边值问题正解的存在性,其中边界条件中含有分数阶导数,并且非线性项 f:［0,1］×［0,+∞)→［0,+∞)满足Caratheodory条件。利用Krasnosel’skii锥上的不动点定理,得到了该边值问题至少存在一个正解和两个正解的充分条件。

关键词: 正解; Caputo导数; 边值问题; 不动点定理

Abstract:

The paper is concerned with the existence of solutions for a class of fractional differential equations boundary value problems with Caputo derivative, where there exist fractional derivative in the boundary conditions and the nonlinear term f:［0,1］×［0,∞)→［0,∞) satisfies Caratheodory conditions.By using the Krasnosel’skii fixed theorem on a cone, the sufficient conditions for the problem at least one and two positive solutions are obtained.

Key words: positive solutions; Caputo derivative; boundary value problems; fixed point theorem

中图分类号:

O175.8

秦小娜,贾梅*,刘帅. 具Caputo导数分数阶微分方程边值问题正解的存在性[J]. J4, 2013, 48(10): 62-67.

QIN Xiao-na, JIA Mei*, LIU Shuai. Existence of positive solutions for fractional differential equations boundary value problems with Caputo derivative[J]. J4, 2013, 48(10): 62-67.

参考文献

相关文章 8

[1]	李凡凡,刘锡平*,智二涛. 分数阶时滞微分方程积分边值问题解的存在性[J]. J4, 2013, 48(12): 24-29.
[2]	俎冠兴. 边值问题的多重正解[J]. J4, 2009, 44(12): 71-76.
[3]	姚庆六. 一类奇异次线性Sturm Liouville 边值问题[J]. J4, 2009, 44(10): 36-38.
[4]	许万银. 一类拟线性Neumann问题的多重解[J]. J4, 2009, 44(10): 39-42.
[5]	代丽美. 正指数Emden-Fowler方程脉冲奇异边值问题的PC¹(［0,1］,R₊)正解[J]. J4, 2008, 43(12): 10-14.
[6]	续晓欣梁月亮桑彦彬. 三阶两点边值问题单调递减正解的存在惟一性[J]. J4, 2008, 43(12): 84-87.
[7]	唐秋云,王明高,刘衍胜 . 高阶p-Laplacian算子方程组边值问题多个正解的存在性[J]. J4, 2008, 43(5): 50-53 .
[8]	徐玲 . 上下解方法与三点边值共振问题的可解性[J]. J4, 2008, 43(5): 66-70 .

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed