Existence of Positive Solutions for Fractional Differential Equation with Nonlocal Boundary Condition

Hongliang Gao and Xiaoling Han

International Journal of Differential Equations, 2011, vol. 2011, 1-10

Abstract:

By using the fixed point theorem, existence of positive solutions for fractional differential equation with nonlocal boundary condition D 0 + α u ( t ) + a ( t ) f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = 0 , u ( 1 ) = ∑ i = 1 ∞ α i u ( ξ i ) is considered, where 1 < α ≤ 2 is a real number, D 0 + α is the standard Riemann-Liouville differentiation, and ξ i ∈ ( 0,1 ) ,   α i ∈ [ 0 , ∞ ) with ∑ i = 1 ∞ α i ξ i α - 1 < 1 , a ( t ) ∈ C ( [ 0,1 ] , [ 0 , ∞ ) ) ,   f ( t , u ) ∈ C ( [ 0,1 ] × [ 0 , ∞ ) , [ 0 , ∞ ) ) .

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:328394

DOI: 10.1155/2011/328394

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