Positive solutions for a boundary-value problem with Riemann-Liouville fractional derivative

被引：8
作者：
Xu, Jiafa [1 ]
Wei, Zhongli [1 ,2 ]
Ding, Youzheng [1 ,2 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
[2] Shandong Jianzhu Univ, Dept Math, Jinan 250101, Shandong, Peoples R China
来源：
LITHUANIAN MATHEMATICAL JOURNAL | 2012年 / 52卷 / 04期
关键词：
fractional boundary-value problem; positive solution; Krasnoselskii-Zabreiko fixed-point theorem; Riemann-Liouville derivative; DIFFERENTIAL-EQUATIONS; EXISTENCE;
D O I：
10.1007/s10986-012-9187-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this work, we are mainly concerned with the existence of positive solutions for the fractional boundary-value problem Here alpha a (2, 3] is a real number, is the standard Riemann-Liouville fractional derivative of order alpha. By virtue of some inequalities associated with the fractional Green function for the above problem, without the assumption of the nonnegativity of f, we utilize the Krasnoselskii-Zabreiko fixed-point theorem to establish our main results. The interesting point lies in the fact that the nonlinear term is allowed to depend on u, u', and .
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收藏
页码：462 / 476
页数：15
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