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.†Reid's primary result was his “Roundabout Theorem†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.
Recommended Citation
C. D. Ahlbrandt et al., "A Discrete Interpretation of Reid's Roundabout Theorem for Generalized Differential Systems," Computers and Mathematics with Applications, Elsevier, Jan 1994.
The definitive version is available at https://doi.org/10.1016/0898-1221(94)00089-1
Department(s)
Mathematics and Statistics
Keywords and Phrases
generalized differential systems; difference equations; discrete Riccati equations; Conjugate points; Reid roundabout theorem
International Standard Serial Number (ISSN)
0898-1221
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 1994 Elsevier, All rights reserved.
Publication Date
01 Jan 1994
