Uniform solvability for families of linear systems on time scales

TL;DR

This paper establishes explicit solvability criteria for families of linear systems on time scales and introduces a novel embedding method into non-autonomous ODEs, advancing the understanding of time scale dynamics.

Contribution

It presents a new embedding technique for time scales into non-autonomous ODEs and provides explicit solvability criteria for linear systems on time scales.

Findings

Explicit solvability criteria for linear systems on time scales

A new embedding method into non-autonomous ODEs

Foundation for structural stability analysis on time scales

Abstract

We give explicit criteria of solvability for families of linear systems on time scales. We introduce a new method of embedding a time scale into a non-autonomous system of ODEs. This will be the first step to implementing the structural stability result obtained by one of the co-authors together with V. A. Pliss to time scale dynamics.