Existence and localization of solutions for fourth-order boundary-value problems

Abstract

In this paper, we study the existence of solutions for the differential equation u(4)(t) = ƒ(t, u(t), u″(t)), where ƒ satisfies one-sided Lipschitz conditions with respect to u and u″, with periodic conditions or boundary conditions from "simply supported" beam theory. We assume the existence of lower and upper solutions (well-ordered and in some cases reversely ordered) and we make use of a fourth-order linear differential operator factorization.