## Abstract and Applied Analysis

### Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity

#### Abstract

We discuss the existence of positive solutions to the following fractional m-point boundary value problem with changing sign nonlinearity ${D}_{0+}^{\alpha }u(t)+\lambda f(t,u(t))=0,0, where $\lambda$ is a positive parameter, $1<\alpha \le 2$, $0<\beta <\alpha -1$, $0<{\xi }_{1}<\cdots <{\xi }_{m-2}<1$ with ${\sum }_{i=1}^{m-2}{\eta }_{i}{\xi }_{i}^{\alpha -\beta -1}<1$, ${D}_{0+}^{\alpha }$ is the standard Riemann-Liouville derivative, $f$ and may be singular at $t=0$ and/or $t=1$ and also may change sign. The work improves and generalizes some previous results.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 214042, 17 pages.

Dates
First available in Project Euclid: 5 April 2013

https://projecteuclid.org/euclid.aaa/1365168373

Digital Object Identifier
doi:10.1155/2012/214042

Mathematical Reviews number (MathSciNet)
MR2955012

Zentralblatt MATH identifier
1247.35192

#### Citation

Wang, Yongqing; Liu, Lishan; Wu, Yonghong. Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 214042, 17 pages. doi:10.1155/2012/214042. https://projecteuclid.org/euclid.aaa/1365168373

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