Solvability of Third-Order Three-Point Boundary Value Problems

We are interested in the existence theorems for a third-order three-point boundary value problem. In the nonresonant case, using the Krasnosel’skii fixed point theorem, we obtain some sufficient conditions for the existence of the positive solutions. In addition, we focus on the resonant case, the b...

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Bibliographic Details
Published inAbstract and Applied Analysis Vol. 2014; no. 2014; pp. 474 - 480-1346
Main Authors Liu, Dongyuan, Ouyang, Zigen
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Wiley
Subjects
Banach spaces
Boundary value problems
Existence theorems
Fixed point theory
Integral equations
Mathematical research
R&D
Research & development
Satellites
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Summary:We are interested in the existence theorems for a third-order three-point boundary value problem. In the nonresonant case, using the Krasnosel’skii fixed point theorem, we obtain some sufficient conditions for the existence of the positive solutions. In addition, we focus on the resonant case, the boundary value problem being transformed into an integral equation with an undetermined parameter, and the existence conditions being obtained by the Intermediate Value Theorem.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/793639