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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 972135, 5 pages
http://dx.doi.org/10.1155/2014/972135
Research Article

Existence of Positive Solutions for an Elastic Beam Equation with Nonlinear Boundary Conditions

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

Received 9 December 2013; Accepted 18 February 2014; Published 20 March 2014

Academic Editor: Ch. Tsitouras

Copyright © 2014 Ruikuan Liu and Ruyun Ma. 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 study the existence and nonexistence of positive solutions for the following fourth-order two-point boundary value problem subject to nonlinear boundary conditions , where are parameters, and , and are continuous. By using the fixed-point index theory, we prove that the problem has at least one positive solution for sufficiently small and has no positive solution for large enough.