Multiplicity of Solutions for a Beam Equation on a Nonlinear Elastic Foundation

In this paper, we investigate a fourth-order differential equation with nonlinear boundary conditions. Multiplicity of solutions for the fourth-order differential equations generated from a nonlinear boundary conditions modeling beams on elastic foundations are considered by variational methods and a three-critical-points theorem. To illustrate the main results, an example is given. This kind of problem arises in the study of deflections of elastic beams on nonlinear elastic foundation. The results we obtain in this paper generalize and improve some known results in literatures.