A third order boundary value problem with one-sided Nagumo condition

Abstract

In this paper we present an existence and location result for the third order separated boundary value problem composed by the differential equation

u′′′(t)=f(t,u(t),u′(t),u′′(t)) with the boundary conditons u(a)=A, u′′(a)=0 and u′′(b)=0, where f:[a,b]×R³→R is a continuous funtion and A∈R. One-sided Nagumo condition, lower and upper solutions, a priori estimates and Leray-Schauder degree play an important role in the arguments.