Abstract
Dynamical equations on time scales are formulated by means of Stieltjes differential equations, which, depending on the time integrator, include ordinary differential equations and difference equations as well as mixtures of both. Explicit conditions for the boundedness and stability of solutions are presented here for linear and nonlinear Stieltjes differential equations. In addition, the continuous dependence of solutions on the time integrator is established by means of a Gronwall-like inequality for equations with different time integrators.
| Original language | English |
|---|---|
| Pages (from-to) | 101-113 |
| Number of pages | 13 |
| Journal | Results in Mathematics |
| Volume | 43 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - 1 Feb 2003 |
Keywords
- 39A10
- 45M10
- Stieltjes differential equations
- boundedness
- continuous dependence on time integrators
- difference equations
- ordinary differential equations
- stability
ASJC Scopus subject areas
- Mathematics (miscellaneous)
- Applied Mathematics