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Dynamic equations on time scales and generalized ordinary differential equations. (English) Zbl 1235.34247
The author presents a procedure how to convert an arbitrary dynamic equation $$ x^\Delta(t) = f(t,x(t)), t \in \mathbb T $$ into a generalized differential equation. This idea of a generalized differential equation is based on the notion of the Kurzweil--Stieltjes or Perron integral. As a byproduct the author shows that some results concerning stability and continuous dependence on parameters drop out of the general setting. In a final section the special case of variational stability is considered.

34N05Dynamic equations on time scales or measure chains
34D05Asymptotic stability of ODE
26A39Special integrals of functions of one real variable
Full Text: DOI
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[9] Schwabik, Š.: Generalized ordinary differential equations, (1992) · Zbl 0781.34003
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