A Discrete Interpretation of Reid's Roundabout Theorem for Generalized Differential Systems
In a series of papers starting with a 1959 paper in J. Math. & Mechanics , W. T. Reid presented Sturmian theory and asymptotic behavior for generalized differential systems. These systems were equivalent to â€œa type of linear vector Riemann-Stieltjes integral equation.â€ Reid's primary result was his â€œRoundabout 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.
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
Mathematics and Statistics
Keywords and Phrases
generalized differential systems; difference equations; discrete Riccati equations; Conjugate points; Reid roundabout theorem
Article - Journal
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