Abstract and Applied Analysis
Volume 2010 (2010), Article ID 694590, 9 pages
doi:10.1155/2010/694590
Research Article

An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction

Yongxiang Li and He Yang

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 28 October 2009; Revised 25 February 2010; Accepted 17 April 2010

Academic Editor: Chaitan Gupta

Copyright © 2010 Yongxiang Li and He Yang. 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 discuss the solvability of the fourth-order boundary value problem u(4)=f(t,u,u′′), 0≤t≤1, u(0)=u(1)=u′′(0)=u′′(1)=0, which models a statically bending elastic beam whose two ends are simply supported, where f:[0,1]×R2→R is continuous. Under a condition allowing that f(t,u,v) is superlinear in u and v, we obtain an existence and uniqueness result. Our discussion is based on the Leray-Schauder fixed point theorem.