[1]李小龙.有序Banach空间非线性分数阶边值问题的正解[J].四川师范大学学报(自然科学版),2020,43(04):475-479.[doi:10.3969/j.issn.1001-8395.2020.04.009]
 LI Xiaolong.Positive Solutions of Nonlinear Fractional Boundary Value Problems in Ordered Banach Spaces[J].Journal of SichuanNormal University,2020,43(04):475-479.[doi:10.3969/j.issn.1001-8395.2020.04.009]
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有序Banach空间非线性分数阶边值问题的正解()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
43卷
期数:
2020年04期
页码:
475-479
栏目:
基础理论
出版日期:
2020-06-20

文章信息/Info

Title:
Positive Solutions of Nonlinear Fractional Boundary Value Problems in Ordered Banach Spaces
文章编号:
1001-8395(2020)04-0475-05
作者:
李小龙
陇东学院 数学与统计学院, 甘肃 庆阳 745000
Author(s):
LI Xiaolong
College of Mathematics and Statistics, Longdong University, Qingyang 745000, Gansu
关键词:
分数阶微分方程 正解 凝聚映射 不动点指数
Keywords:
fractional differential equation positive solution condensing mapping fixed point index
分类号:
O175.15
DOI:
10.3969/j.issn.1001-8395.2020.04.009
文献标志码:
A
摘要:
讨论有序Banach空间E中分数阶边值问题Dα0+u(t)=f(t,u(t)), 0< t< 1, u(0)=u(1)=u'(0)=u'(1)=θ正解的存在性,其中,3<α≤4,Dα0+是标准的Riemann-Liouville微分,f:[0,1]×P→P连续,P为E中的正元锥.通过非紧性测度的估计技巧与凝聚映射的不动点指数理论获得该边值问题正解的存在性结果.
Abstract:
The existence of positive solutions for a fractional boundary value problemDα0+u(t)=f(t,u(t)), 0< t<1, u(0)=u(1)=u'(0)=u'(1)=θin an ordered Banach spaces E is discussed, where 3<α≤4, Dα0+ is the standard Riemann-Liouville differentiation, f:[0,1]× P→P is continuous, and P is the cone of positive elements in E. An existence result of positive solutions is obtained by employing a new estimate of noncompactness measure and the fixed point index theory of condensing mapping.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2018-09-18 接受日期:2019-04-10
基金项目:国家自然科学基金(11561038和11661051)和甘肃省自然科学基金(18JR3RM238)
作者简介:李小龙(1976—),男,副教授,主要从事抽象微分方程及其应用的研究,E-mail:lixl80@163.com
更新日期/Last Update: 2020-06-20