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

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.