Existence and uniqueness results for the bending elastic beam equations

Abstract

We examine the existence and uniqueness of solutions to a particular class of two-point boundary value problems involving fourth-order ordinary differential equations. These problems have fascinating applications in the modeling of deflections of beams. Applying the fixed point theorems by Banach and Rus is one of the main instruments used in this investigation. Our theoretical findings are applied to deflections of an elastic beam when subjected to a loading force with both ends hinged. We also ensure the existence and uniqueness of solutions to the model for certain classes of linear and nonlinear loading forces.