On the sign of Green’s functions for multipoint boundary value problems

Abstract

If an nth order linear ordinary differential equation Ly -0 is disconjugate, then the sign of the Green's functions is well known. In this work, it is only supposed that Ly = 0 is ("i > > ifc)-disconjugate for certain values of i lf ,4, and the sign of the Green's functions for certain multipoint problems is shown to be the same as when Ly = 0 is disconjugate. The results extend earlier ones on two-point problems due to Peterson. The proofs simplify Peterson's arguments in a way such that the analysis of two-point problems is not only easier but carriers over to multipoint problems.