Title

A Discrete Interpretation of Reid's Roundabout Theorem for Generalized Differential Systems

Abstract

In a series of papers starting with a 1959 paper in J. Math. & Mechanics [1], W. T. Reid presented Sturmian theory and asymptotic behavior for generalized differential systems. These systems were equivalent to “a type of linear vector Riemann-Stieltjes integral equation.â€ Reid's primary result was his “Roundabout Theoremâ€ for this generalized setting. As he pointed out, if the measure is piecewise constant, then results for difference equations ensue. The objectives of this study are (i)to interpret Reid's results for both Jacobi and Riccati difference equations and (ii)to compare those results with subsequent studies of difference equations based on discrete variational theory.

Department(s)

Mathematics and Statistics

Keywords and Phrases

generalized differential systems; difference equations; discrete Riccati equations; Conjugate points; Reid roundabout theorem

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1994 Elsevier, All rights reserved.

Share

 
COinS