Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 1, Pages 29-46
doi:10.1155/S1048953395000037

A sturm separation theorem for a linear 2nth order self-adjoint differential equation

Charles T. Fulton,1 Limin Wu,1 and Steven Pruess2

1Program of Applied Mathematics, Florida Institute of Technology, Melbourne 32901-6988, FL, USA
2Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden 80401-1887, CO, USA

Received 1 January 1993; Revised 1 October 1994

Copyright © 1995 Charles T. Fulton et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For the 2nth order equation, (−1)nv(2n)+qv=0, with q continuous, we obtain a Sturm Separation theorem, involving n+1 solutions of the equation, which is somewhat analogous to the classical result that the zeros of two linearly independent solutions of the second order equation separate each other.