A discrete interpretation of Reid’s roundabout theorem for generalized differential systems. (English) Zbl 0805.93024
Summary: In a series of paper starting with a paper in J. Math. Mech. 8, 705-726 (1959; Zbl 0094.060), 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.
MSC:
| 93C15 | Control/observation systems governed by ordinary differential equations |
Citations:
Zbl 0094.060References:
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