Dynamic equations on time scales: a survey

Abstract

In this paper we derive a system of differential equations on time scales of the Solow type corresponding to a production function depending on several capitals. A sufficient condition for the exponential stability of the steady-state solution with positive coordinates is proved. The obtained results are applied to the case of the Cobb-Douglas type production function. Mathematics subject classification (2010): 34N05, 26E70, 97E40, 97M10.

Transition matrix and generalized matrix exponential via the Peano-Baker series

“…The material in this Appendix is drawn mainly from [4]. A succinct survey on time scales can be found in [2].…”

Generalizations of Gronwall–Bihari inequalities on time scales

“…Since then, the theory has been growing up and applied to many different fields of mathematics [1,5,6]. We refer the reader to [5] for all the basic definitions and results on time scales necessary to this work (e.g., delta differentiability, rd-continuity, exponential function and its properties).…”

Oscillation of third-order quasilinear neutral dynamic equations on time scales with distributed deviating arguments

“…The theory of time scales, which has recently received a lot of attention, was introduced by Hilger [9], in order to unify continuous and discrete analysis. Since then, several authors have expounded on various aspects of this new theory; see the survey paper by Agarwal et al [1]. A book on the subject of time scales by Bohner and Peterson [3] also summarizes and organizes much of the time scale calculus.…”