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Abstract and Applied Analysis
Volume 2014, Article ID 131548, 14 pages
http://dx.doi.org/10.1155/2014/131548
Research Article

The Existence of Positive Solutions for Fractional Differential Equations with Integral and Disturbance Parameter in Boundary Conditions

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 13 November 2013; Accepted 17 January 2014; Published 24 March 2014

Academic Editor: Paul Eloe

Copyright © 2014 Mei Jia and Xiping Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the existence and nonexistence of the positive solutions for the integral boundary value problem of the fractional differential equations with the disturbance parameter in the boundary conditions and the impact of the disturbance parameter on the existence of positive solutions. By using the upper and lower solutions method, fixed point index theory and the Schauder fixed point theorem, we obtain sufficient conditions for that the problem has at least one positive solution, two positive solutions and no solutions. Under certain conditions, we also obtain the demarcation point which divides the disturbance parameters into two subintervals such that the boundary value problem has positive solutions for the disturbance parameter in one subinterval while no positive solutions in the other.