Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter

This paper is concerned with the following second-order three-point boundary value problem u″t+β2ut+λqtft,ut=0, t∈0 , 1, u0=0, u(1)=δu(η), where β∈(0,π/2), δ>0, η∈(0,1), and λ is a positive parameter. First, Green’s function for the associated linear boundary value problem is constructed, and the...

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Published inJournal of Applied Mathematics Vol. 2014; no. 2014; pp. 707 - 714-573
Main Authors Liu, Jian, Feng, Hanying, Feng, Xingfang
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
Hindawi Limited
Wiley
Subjects
Boundary value problems
Construction
Green's functions
Mathematical analysis
Optimization
Studies
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Summary:This paper is concerned with the following second-order three-point boundary value problem u″t+β2ut+λqtft,ut=0, t∈0 , 1, u0=0, u(1)=δu(η), where β∈(0,π/2), δ>0, η∈(0,1), and λ is a positive parameter. First, Green’s function for the associated linear boundary value problem is constructed, and then some useful properties of Green’s function are obtained. Finally, existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values of λ by means of the fixed point index theory.
Bibliography:ObjectType-Article-1
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content type line 23
ISSN:1110-757X
1687-0042
DOI:10.1155/2014/603203