Summary: This paper investigates the boundary value problem for an elastic beam equation of the form
with the boundary conditions
The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. By using Leray-Schauder nonlinear alternative, Leray-Schauder fixed point theorem and a fixed point theorem due to R. I. Avery and A. C. Peterson [Comput. Math. Appl. 42, No. 3–5, 313–322 (2001; Zbl 1005.47051)], we establish some results on the existence and the multiplicity of positive solutions to the boundary value problem.