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Journal of Function Spaces
Volume 2017, Article ID 1069491, 8 pages
https://doi.org/10.1155/2017/1069491
Research Article

S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation

1Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, China

Correspondence should be addressed to Ruyun Ma; nc.ude.unwn@yram

Received 1 December 2016; Accepted 20 June 2017; Published 24 July 2017

Academic Editor: Gennaro Infante

Copyright © 2017 Jinxiang Wang 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 investigate the existence of -shaped connected component in the set of positive solutions of the fourth-order boundary value problem: , , where is a parameter, , and with . We develop a bifurcation approach to deal with this extreme situation by constructing a sequence of functions satisfying and By studying the auxiliary problems, we get a sequence of unbounded connected components , and, then, we find an unbounded connected component in the set of positive solutions of the fourth-order boundary value problem which satisfies and is -shaped.