Absolute continuity and existence of solutions to dynamic inclusions in time scales
The authors provide results about the existence of solutions to a system of dynamical inclusions on time scales. There are several preparatory sections about certain notions for time scales, such as absolute continuity, Euler solutions, measurability, semi-continuity, Gronwall inequality. The main theorem then states that an initial value problem associated to the dynamic equation \[ x^\Delta(t) \in F(t,x(t)) \quad\text{a.e.} \] with appropriate properties of the multifunction \(F\) has a solution.
scientific article; zbMATH DE number 6168457
scientific article