Existence, nonexistence and multiplicity results for some beam equations

Abstract

This paper studies some fourth order nonlinear fully equations with a parameter s ∈ R, with two point boundary conditions. These problems model several phenomena, such as, a cantilevered beam with a linear relation between the curvature and the shear force at both endpoints. For some values of the real constants, it will be presented an Ambrosetti–Prodi type discussion on s. The arguments used apply lower and upper solutions technique, a priori estimations and topological degree theory.