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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 621315, 8 pages
http://dx.doi.org/10.1155/2013/621315
Research Article

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

College of Electron and Information, Zhejiang University of Media and Communications, Hangzhou, Zhejiang 310018, China

Received 1 March 2013; Revised 12 June 2013; Accepted 14 June 2013

Academic Editor: Chuanzhi Bai

Copyright © 2013 Yongping Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.