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2014 The Existence of Positive Solutions for Fractional Differential Equations with Integral and Disturbance Parameter in Boundary Conditions
Mei Jia, Xiping Liu
Abstr. Appl. Anal. 2014: 1-14 (2014). DOI: 10.1155/2014/131548

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 a in the boundary conditions and the impact of the disturbance parameter a 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.

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Mei Jia. Xiping Liu. "The Existence of Positive Solutions for Fractional Differential Equations with Integral and Disturbance Parameter in Boundary Conditions." Abstr. Appl. Anal. 2014 1 - 14, 2014. https://doi.org/10.1155/2014/131548

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07021775
MathSciNet: MR3191018
Digital Object Identifier: 10.1155/2014/131548

Rights: Copyright © 2014 Hindawi

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