Green’s function inequalities for two-point boundary value problems

Peter W. Bates and Grant Bernard Gustafson

Vol. 59 (1975), No. 2, 327–343

DOI: 10.2140/pjm.1975.59.327

Abstract

Simple inequalities are obtained for the Green’s function G(t,s) of a two-point boundary value problem for a k-th order linear ordinary differential equation. The constants appearing in the inequalities are best possible. Each estimate has right side a product of a function of t and a function of s. Illustrations are given for k = 2,3,4 and certain k-th order constant coefficient operators.

Mathematical Subject Classification 2000

Primary: 34B05

Secondary: 34C10

Milestones

Received: 21 March 1975

Revised: 18 June 1975

Published: 1 August 1975