Abstract and Applied Analysis

Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments

Zhaocai Hao and Yubo Huang

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Abstract

We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments D α x ( t ) + μ h ( t ) f ( x ( a ( t ) ) ) = 0 , t ( 0,1 ) , 2 < α 3 , μ > 0 , x ( 0 ) = x ( 0 ) = 0 , x ( 1 ) = β x ( η ) + λ [ x ] , β > 0 , and   η ( 0,1 ) , where D α is the standard Riemann-Liouville derivative, f : [ 0 , ) [ 0 , ) is continuous, f ( 0 ) > 0 ,  h  : [ 0,1 ] ( , + ) , and a ( t ) is the advanced argument. Our analysis relies on a nonlinear alternative of Leray-Schauder type. An example is given to illustrate our results.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 158436, 7 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412279715

Digital Object Identifier
doi:10.1155/2014/158436

Mathematical Reviews number (MathSciNet)
MR3232822

Zentralblatt MATH identifier
07021833

Citation

Hao, Zhaocai; Huang, Yubo. Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 158436, 7 pages. doi:10.1155/2014/158436. https://projecteuclid.org/euclid.aaa/1412279715


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