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Nonlocal boundary value problem for fractional differential equations with p ‐Laplacian
Author(s) -
Zhi Ertao,
Liu Xiping,
Li Fanfan
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3005
Subject(s) - mathematics , multiplicity (mathematics) , fixed point theorem , boundary value problem , p laplacian , laplace operator , operator (biology) , cone (formal languages) , mathematical analysis , pure mathematics , biochemistry , chemistry , repressor , algorithm , transcription factor , gene
In this paper, we are concerned with the existence of positive solutions for the following nonlocal BVP of fractional DEs with p ‐Laplacian operatorϕ pD0 +α u ( t )′ ′ = f t , u ( t ) , D 0 + β u ( t ), t ∈ 0 , 1 ,u ( 0 ) = u ′ ′ ( 0 ) = 0 , u ( 1 ) = ∫ 0 1 g ( s ) u ( s ) d s ,ϕ pD0 +α u ( 0 )′ = λ 1ϕ pD 0 + α u (ξ 1)′ ,ϕ pD 0 + α u ( 1 )= λ 2ϕ pD 0 + α u (ξ 2).By using the fixed point theorem in a cone, multiplicity solutions of the BVP are obtained. An example is also given to show the effectiveness of the obtained result. Copyright © 2013 John Wiley & Sons, Ltd.