Positive Solutions for Multipoint Boundary Value Problem of Fractional Differential Equations

Wenyong Zhong

Abstract and Applied Analysis, 2010, vol. 2010, 1-15

Abstract:

We study the existence and multiplicity of positive solutions for the fractional m -point boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ' ( 0 ) = 0 , u ' ( 1 ) = ∑ i = 1 m - 2 a i u ' ( ξ i ) , where 2 < α < 3 , D 0 + α 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 Ï = ∑ i = 1 m - 2 a i ξ i α - 2 with Ï < 1 . In light of some fixed point theorems, some existence and multiplicity results of positive solutions are obtained.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:601492

DOI: 10.1155/2010/601492

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