On the solvability of some fourth-order equations with functional boundary conditions

Abstract

In this paper it is considered a fourth order problem composed of a fully nonlinear differential equation and functional boundary conditions satisfying some monotone conditions.This functional dependence on u; u0 and u00and generalizes several types of boundary conditions such as Sturm-Liouville, multipoint, maximum and/or minimum arguments, or nonlocal. The main theorem is an existence and location result as it provides not only the existence, but also some qualitative information about the solution.