Existence and location of solutions to fourth-order Lidstone coupled systems with dependence on odd derivatives

Abstract

This paper addresses the existence and location results for coupled system with two fourth-order differential equations with dependence on all derivatives in nonlinearities and subject to Lidstone-type boundary conditions. To guarantee the existence and location of the solutions, we applied lower and upper solutions technique and degree theory. In this context, we highlight a new type of Nagumo condition to control the growth of the third derivatives and increases the number of applications, as well as a new type of definitions of upper and lower solutions for such coupled systems. Last section contains an application to a coupled system composed by two fourth order equations, which models the estimated bending of simply-supported beam with torsional solitons.