Boundary Value Problems
Volume 2011 (2011), Article ID 594128, 21 pages
doi:10.1155/2011/594128
Research Article

Eigenvalue Problem and Unbounded Connected Branch of Positive Solutions to a Class of Singular Elastic Beam Equations

Huiqin Lu

School of Mathematical Sciences, Shandong Normal University, Jinan, 250014 Shandong, China

Received 16 October 2010; Revised 22 December 2010; Accepted 27 January 2011

Academic Editor: Kanishka Perera

Copyright © 2011 Huiqin Lu. 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

This paper investigates the eigenvalue problem for a class of singular elastic beam equations where one end is simply supported and the other end is clamped by sliding clamps. Firstly, we establish a necessary and sufficient condition for the existence of positive solutions, then we prove that the closure of positive solution set possesses an unbounded connected branch which bifurcates from ( 0 , 𝜃 ) . Our nonlinearity 𝑓 ( 𝑡 , 𝑢 , 𝑣 , 𝑤 ) may be singular at 𝑢 , 𝑣 , 𝑡 = 0 and/or 𝑡 = 1 .