Solvability of boundary value problems of nonlinear fractional differential equations

被引：5

作者：

Chen, Weiqi ^{[1
,2
]}

Zhao, Yige ^{[3
]}

机构：

[1] Shandong Univ, Sch Econ, Jinan 250100, Shandong, Peoples R China

[2] Shandong Univ, Sch Phys Educ, Jinan 250061, Shandong, Peoples R China

[3] Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Shandong, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2015年

基金：

中国国家自然科学基金;

关键词：

fractional differential equation; boundary value problem; positive solution; fractional Green's function; fixed point theorem; lower and upper solution method; MULTIPLE POSITIVE SOLUTIONS; EXISTENCE; UNIQUENESS;

D O I：

10.1186/s13662-015-0373-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the existence of multiple positive solutions for the nonlinear fractional differential equation boundary value problem D(0+)(alpha)u(t) + f (t, u(t)) = 0, 0 < t < 1, u(0) = u(1) = u' (0) = 0, where 2 < alpha <= 3 is a real number, D-0+(alpha) is the Riemann-Liouville fractional derivative. By the properties of the Green's function, the lower and upper solution method and the Leggett-Williams fixed point theorem, some new existence criteria are established. As applications, examples are presented to illustrate the main results.

引用

页码：1 / 13

页数：13

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