Ważewski theorem on time scales with a set of egress points that is not the whole boundary

Ważewski type theorem for non-autonomous systems of equations with a disconnected set of egress points

“…The result given here generalizes the result in [12] of the first and second author, where the planar dynamic system on time scales is studied. Moreover, it generalizes the result in [8] of the third author and J. Diblík, where the system of n dynamic equations on time scales is studied with of a simple hyper-prism shape.…”

“…Are there any sufficiently general and more easily verifiable conditions (see [12] for n = 2)? • The main result of our paper allows to consider systems with disconnected sets of egress points that differ in points with non-zero graininess.…”

“…Now, we are ready to define a local -process on time scales, which is analogy of local process in a continuous case, see, e.g., [16,17]. The following two definitions are taken from [12]. Definition 2.6.…”

“…The following proposition can be found in [12], and it says about a preservation (analogously as in R) of homeomorphisms along trajectories. …”

“…[4][5][6]. Finally and recently, it was used for dynamic equations on time scales, see e.g., [1,[7][8][9][10]12].…”