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Open Access Research Article

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

Huiqin Lu

Author Affiliations

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

Boundary Value Problems 2011, 2011:594128  doi:10.1155/2011/594128

Published: 21 February 2011

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 Our nonlinearity may be singular at and/or .