Fourth order functional boundary value problems: Existence results and extremal solutions

Abstract

In this work we present two types of results for some fourth order functional boundary value problems. The first one presents an existence and location result for a problem where every boundary conditions have functional dependence. The second one states sufficient conditions for the existence of extremal solutions for functional problems with more restrict boundary functions. The arguments make use of lower and upper solutions technique, a Nagumo-type condition,an adequate version of Bolzano’s theorem and existence of extremal fixed points for a suitable mapping.