Abstract and Applied Analysis

On the Existence of Positive Solutions of Resonant and Nonresonant Multipoint Boundary Value Problems for Third-Order Nonlinear Differential Equations

Liu Yang, Chunfang Shen, Dapeng Xie, and Xiping Liu

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Abstract

Positive solutions for a kind of third-order multipoint boundary value problem under the non-resonant conditions and the resonant conditions are considered. In the nonresonant case, by using Leggett-Williams fixed-point theorem, the existence of at least three positive solutions is obtained. In the resonant case, by using Leggett-Williams norm-type theorem due to O’Regan and Zima, existence result of at least one positive solution is established. The results obtained are valid and new for the problem discussed. Two examples are given to illustrate the main results.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 687595, 12 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512211

Digital Object Identifier
doi:10.1155/2013/687595

Mathematical Reviews number (MathSciNet)
MR3143562

Zentralblatt MATH identifier
1280.34028

Citation

Yang, Liu; Shen, Chunfang; Xie, Dapeng; Liu, Xiping. On the Existence of Positive Solutions of Resonant and Nonresonant Multipoint Boundary Value Problems for Third-Order Nonlinear Differential Equations. Abstr. Appl. Anal. 2013 (2013), Article ID 687595, 12 pages. doi:10.1155/2013/687595. https://projecteuclid.org/euclid.aaa/1393512211


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