Existence and uniqueness of solutions to the nonlinear boundary value problem for fourth-order differential equations with all derivatives

Abstract

This article addresses the existence and uniqueness of solution for fully fourth-order differential equations modeling beams on elastic foundations with nonlinear boundary conditions. The proof will rely on Perov’s fixed point theorem in complete generalized metric spaces to overcome the problems due to the presence of all lower-order derivatives in the nonlinearity. Finally, some illustrating examples of the theory are presented.