Abstract and Applied Analysis

Successive Iteration of Positive Solutions for Fourth-Order Two-Point Boundary Value Problems

Yongping Sun, Xiaoping Zhang, and Min Zhao

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Abstract

We are concerned with a fourth-order two-point boundary value problem. We prove the existence of positive solutions and establish iterative schemes for approximating the solutions. The interesting point of our method is that the nonlinear term is involved with all lower-order derivatives of unknown function, and the iterative scheme starts off with a known cubic function or the zero function. Finally we give two examples to verify the effectiveness of the main results.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 621315, 8 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511962

Digital Object Identifier
doi:10.1155/2013/621315

Mathematical Reviews number (MathSciNet)
MR3073510

Zentralblatt MATH identifier
07095178

Citation

Sun, Yongping; Zhang, Xiaoping; Zhao, Min. Successive Iteration of Positive Solutions for Fourth-Order Two-Point Boundary Value Problems. Abstr. Appl. Anal. 2013 (2013), Article ID 621315, 8 pages. doi:10.1155/2013/621315. https://projecteuclid.org/euclid.aaa/1393511962


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