Multiple Nontrivial Solutions for a Floating Beam Equation via Critical Point Theory

Abstract

We study periodic flexings of a floating beam via critical point theory. The beam is described by the nonlinear equation with free-end boundary conditions described in the Introduction. We give a theorem of existence of two nontrivial solutions and a theorem of existence of four nontrivial solutions, depending on the position of a suitable parameter with respect to the eigenvalues of the linear part.