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.


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