New results on the sign of the Green function of a two-point n-th order linear boundary value problem

Abstract

This paper provides conditions for determining the sign of all the partial derivatives of the Green functions of n-th order boundary value problems subject to a wide set of homogeneous two-point boundary conditions, removing restrictions of previous results about the distance between the two extremes that define the problem. To do so, it analyzes the sign of the derivatives of the solutions of related two-point n-th order boundary value problems subject to n-1 boundary conditions by introducing a new property denoted by ‘hyperdisfocality’.