Vol. 92, No. 1, 1981

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

Jerry Ridenhour

Vol. 92 (1981), No. 1, 141–150
Abstract

If an n-th 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 (i1,,ik)-disconjugate for certain values of i1,,ik, 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.

Mathematical Subject Classification 2000
Primary: 34B27
Secondary: 34B10
Milestones
Received: 26 February 1979
Revised: 6 August 1979
Published: 1 January 1981
Authors
Jerry Ridenhour