Existence of positive solutions of third-order boundary value problems with integral boundary conditions in Banach spaces

This paper deals with positive solutions of a third-order differential equation in ordered Banach spaces, ( φ ( − x ″ ( t ) ) ) ′ = f ( t , x ( t ) ) , t ∈ J , subject to the following integral boundary conditions: x ( 0 ) = θ , x ″ ( 0 ) = θ , x ( 1 ) = ∫ 0 1 g ( t ) x ( t ) d t , where θ is the ze...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2013; no. 1
Main Authors: Fu, Dan, Ding, Wei
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 20.03.2013
Subjects:
Analysis
Difference and Functional Equations
Functional Analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Progress in Functional Differential and Difference Equations
positive solutions
fixed-point principle
measure of noncompactness
cone
boundary-value problem
ISSN:1687-1847, 1687-1847
Online Access:Get full text
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Summary:This paper deals with positive solutions of a third-order differential equation in ordered Banach spaces, ( φ ( − x ″ ( t ) ) ) ′ = f ( t , x ( t ) ) , t ∈ J , subject to the following integral boundary conditions: x ( 0 ) = θ , x ″ ( 0 ) = θ , x ( 1 ) = ∫ 0 1 g ( t ) x ( t ) d t , where θ is the zero element of E , g ∈ L [ 0 , 1 ] is nonnegative, φ : R → R is an increasing and positive homomorphism, and φ ( 0 ) = θ 1 . The arguments are based upon the fixed-point principle in cone for strict set contraction operators. Meanwhile, as an application, we also give an example to illustrate our results.
ISSN:1687-1847
1687-1847
DOI:10.1186/1687-1847-2013-65