Positive solutions for a class of fractional 3-point boundary value problems at resonance

Wang, Y.; Liu, Lishan

doi:10.1186/s13662-016-1062-5

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Open access

Authors

Wang, Y.

Liu, Lishan

Date

2017

Type

Journal Article

Metadata

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Citation

Wang, Y. and Liu, L. 2017. Positive solutions for a class of fractional 3-point boundary value problems at resonance. Advances in Difference Equations. 2017 (1).

Source Title

Advances in Difference Equations

DOI

10.1186/s13662-016-1062-5

ISSN

1687-1839

School

Department of Mathematics and Statistics

Abstract

In this paper, we study the nonlocal fractional differential equation: {Dα0+u(t)+f(t,u(t))=0,0<t<1,u(0)=0,u(1)=ηu(ξ), where 1<α<2, 0<ξ<1, ηξα−1=1, Dα0+ is the standard Riemann-Liouville derivative, f:[0,1]×[0,+∞)→R is continuous. The existence and uniqueness of positive solutions are obtained by means of the fixed point index theory and iterative technique.

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