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Mathematical Problems in Engineering
Volume 2011, Article ID 609189, 9 pages
Research Article

Monotone Positive Solutions for an Elastic Beam Equation with Nonlinear Boundary Conditions

Department of Applied Mathematics, Lanzhou University of Technology, Gansu, Lanzhou 730050, China

Received 19 April 2011; Accepted 2 August 2011

Academic Editor: Angelo Luongo

Copyright © 2011 Jian-Ping Sun and Xian-Qiang Wang. 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.


This paper is concerned with the existence of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions. By applying monotone iteration method, we not only obtain the existence of monotone positive solutions but also establish iterative schemes for approximating the solutions. It is worth mentioning that these iterative schemes start off with zero function or quadratic function, which is very useful and feasible for computational purpose. An example is also included to illustrate the main results obtained.