Vector Fixed Point Theorem with Application to Systems of Nonlinear Elastic Beams Equations

Abstract

In this work, we establish a new existence and uniqueness of vector fixed point for a class of sum-type vector operators with some mixed monotone property in partially ordered product Banach spaces. The technique used is Thompson’s part metric, and our goal is to extend and improve existing works in the scalar case vector case. As an application, we study the existence and uniqueness of solutions for systems of nonlinear singular fourth-order elastic beam equations with nonlinear boundary conditions.