Abstract and Applied Analysis
Volume 2010 (2010), Article ID 601492, 15 pages
doi:10.1155/2010/601492
Research Article

Positive Solutions for Multipoint Boundary Value Problem of Fractional Differential Equations

Wenyong Zhong

School of Mathematics and Computer Sciences, Jishou University, 120 Renmin South Road, Jishou, Hunan 416000, China

Received 28 August 2010; Revised 10 December 2010; Accepted 16 December 2010

Academic Editor: Ferhan M. Atici

Copyright © 2010 Wenyong Zhong. 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 multiplicity of positive solutions for the fractional 𝑚 -point boundary value problem 𝐷 𝛼 0 + 𝑢 ( 𝑡 ) + 𝑓 ( 𝑡 , 𝑢 ( 𝑡 ) ) = 0 , 0 < 𝑡 < 1 , 𝑢 ( 0 ) = 𝑢 ( 0 ) = 0 , 𝑢 ∑ ( 1 ) = 𝑚 − 2 𝑖 = 1 𝑎 𝑖 𝑢 ( 𝜉 𝑖 ) , where 2 < 𝛼 < 3 , 𝐷 𝛼 0 + is the standard Riemann-Liouville fractional derivative, and 𝑓 ∶ [ 0 , 1 ] × [ 0 , ∞ ) ↦ [ 0 , ∞ ) is continuous. Here, 𝑎 𝑖 ⩾ 0 for 𝑖 = 1 , … , 𝑚 − 2 , 0 < 𝜉 1 < 𝜉 2 < ⋯ < 𝜉 𝑚 − 2 < 1 , and ∑ 𝜌 = 𝑚 − 2 𝑖 = 1 𝑎 𝑖 𝜉 𝑖 𝛼 − 2 with 𝜌 < 1 . In light of some fixed point theorems, some existence and multiplicity results of positive solutions are obtained.