Measure differential equations: differentiability of solutions with respect to initial conditions. (English) Zbl 1363.34033
Summary: Under some conditions, we know that measure differential equations are equivalent to the generalized ordinary differential equations, so we can apply some results of generalized differential equations in the measure differential equations. The differentiability of solutions with respect to initial conditions for measure differential equations is established in this paper by using the differentiability of solutions with respect to initial conditions for generalized ordinary differential equations.
MSC:
34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
28A15 | Abstract differentiation theory, differentiation of set functions |
26A39 | Denjoy and Perron integrals, other special integrals |