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

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 .