Stability and boundedness of solutions of Stieltjes Differential Equations
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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 Classifications45M10 39A10
KeywordsStieltjes differential equations difference equations ordinary differential equations boundedness stability continuous dependence on time integrators
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