## On $$x'=f(t,x)$$ and Henstock-Kurzweil integrals.(English)Zbl 0733.34004

The authors take into consideration the Cauchy problem $$x'=f(t,x),\quad x(\tau)=\xi,$$ in Henstock-Kurzweil integral setting. More precisely, they prove an existence result which extends the Carathéodory theorem and a continuous dependence result with respect to a parameter. Examples are given to illustrate these results.

### MSC:

 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 34A99 General theory for ordinary differential equations