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Results in Mathematics

, Volume 43, Issue 1–2, pp 101–113 | Cite as

Stability and boundedness of solutions of Stieltjes Differential Equations

  • M. I. Gil’
  • P. E. Kloeden
Article
  • 55 Downloads

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.

AMS Subject Classifications

45M10 39A10 

Keywords

Stieltjes differential equations difference equations ordinary differential equations boundedness stability continuous dependence on time integrators 

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Copyright information

© Birkhäuser Verlag, Basel 2003

Authors and Affiliations

  1. 1.Department of MathematicsBen Gurion University of the NegevBeer-ShevaIsrael
  2. 2.FB MathematikJohann Wolfgang Goethe UniversitätFrankfurt am MainGermany

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