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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

${x}^{{\Delta }}\left(t\right)=f\left(t,x\left(t\right)\right),t\in 𝕋$

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.

##### MSC:
 34N05 Dynamic equations on time scales or measure chains 34D05 Asymptotic stability of ODE 26A39 Special integrals of functions of one real variable
##### References:
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