Dynamic equations on time scales and generalized ordinary differential equations (Q641610)

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.