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.
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This work was partly supported by the Israel Ministry of Science and Technology and by the DFG Forschungsschwerpunkt “Ergodentheorie, Analysis und effiziente Simulation dynamischer Systeme”.
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Gil’, M.I., Kloeden, P.E. Stability and boundedness of solutions of Stieltjes Differential Equations. Results. Math. 43, 101–113 (2003). https://doi.org/10.1007/BF03322726
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DOI: https://doi.org/10.1007/BF03322726