Generalized differential equations: differentiability of solutions with respect to initial conditions and parameters
The author proves the differentiability of solutions of generalized differential equations with respect to initial conditions and parameters. The term generalized differential equation means a nonlinear integral equation involving the Kurzweil integral. The present results extend the work by \textit{J. Kurzweil} [Czech. Math. J. 7(82), 418--449 (1957; Zbl 0090.30002)] and \textit{Š Schwabik} [Generalized ordinary differential equations. Singapore: World Scientific (1992; Zbl 0781.34003)]. They also unify the differentiability properties of solutions for differential equations with impulses or for dynamic equations on time scales. The proof of the main result is based on the arguments of \textit{R. Hilscher, V. Zeidan} and \textit{W. Kratz} [``Differentiation of solutions of dynamic equations on time scales with respect to parameters'', Adv. Dyn. Syst. Appl. 4, No. 1, 35--54 (2009), \url{http://campus.mst.edu/adsa}].
generalized ordinary differential equations
scientific article; zbMATH DE number 6156121