Les families de fonctions conduisant aux équations différentielles implicites par rapport à la dérivée.
In the paper existence and uniqueness results for the linear differential system on the interval [0,1] with distributional coefficients and solutions from the space of regulated functions are obtained.
The paper deals with the linear differential equation (0.1) with distributional coefficients and solutions from the space of regulated functions. Our aim is to get the basic existence and uniqueness results for the equation (0.1) and to generalize the known results due to F. V. Atkinson [At], J. Ligeza [Li1]-[Li3], R. Pfaff ([Pf1], [Pf2]), A. B. Mingarelli [Mi] as well as the results from the paper [Pe-Tv] concerning the equation (0.1).
In the paper we consider lower semicontinuous differential inclusions with one sided Lipschitz and compact valued right hand side in a Banach space with uniformly convex dual. We examine the nonemptiness and some qualitative properties of the solution set.