The upper and lower solution method for nonlinear fourth-order boundary value problem

in this paper, we study the existence of a solution for a fourth order boundary value problem Where f ∈ C([0,l]× IR2, IR), and f ∈ C([0,l]× IR3, IR). By placing certain restrictions on the nonlinear term f, we prove the existence of at least one solution to the boundary-value problem with the use of...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 285; no. 1; pp. 012016 - 7
Main Author El-Haffaf, Amir
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.03.2011
Subjects
Boundary value problems
Constrictions
Construction
Existence theorems
Fixed points (mathematics)
Mathematical analysis
Nonlinearity
Physics
Placing
Schauder fixpoint theorem
Theorems
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ISSN1742-6596
1742-6588
1742-6596
DOI10.1088/1742-6596/285/1/012016

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Summary:in this paper, we study the existence of a solution for a fourth order boundary value problem Where f ∈ C([0,l]× IR2, IR), and f ∈ C([0,l]× IR3, IR). By placing certain restrictions on the nonlinear term f, we prove the existence of at least one solution to the boundary-value problem with the use of lower and upper solution method and Schauder fixed-point theorem. The construction of lower or upper solutions is also presented.
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ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/285/1/012016