## Abstract and Applied Analysis

### Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems

#### Abstract

We are concerned with the following nonlinear three-point fractional boundary value problem: ${D}_{0+}^{\alpha }u(t)+\lambda a(t)f(t,u(t))=0$, $0, $u(0)=0$, and $u(1)=\beta u(\eta )$, where $1<\alpha \le 2$, $0<\beta <1$, $0<\eta <1$, ${D}_{0+}^{\alpha }$ is the standard Riemann-Liouville fractional derivative, $a(t)>0$ is continuous for $0\le t\le 1$, and $f\ge 0$ is continuous on $[0,1]{\times}[0,\infty )$. By using Krasnoesel'skii's fixed-point theorem and the corresponding Green function, we obtain some results for the existence of positive solutions. At the end of this paper, we give an example to illustrate our main results.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 602604, 8 pages.

Dates
First available in Project Euclid: 27 February 2015

https://projecteuclid.org/euclid.aaa/1425048241

Digital Object Identifier
doi:10.1155/2014/602604

Mathematical Reviews number (MathSciNet)
MR3214439

Zentralblatt MATH identifier
07022702

#### Citation

Liu, Hongjie; Fu, Xiao; Qi, Liangping. Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 602604, 8 pages. doi:10.1155/2014/602604. https://projecteuclid.org/euclid.aaa/1425048241

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