On the non--multiplicity of solutions to matrix equations on time scales

TL;DR

This paper proves that first-order matrix dynamic equations on time scales have unique solutions under certain conditions, extending previous theories to more complex matrix systems with generalized Lipschitz criteria.

Contribution

It introduces new conditions ensuring the uniqueness of solutions for complex matrix systems on time scales, expanding existing mathematical frameworks.

Findings

Established non-multiplicity (uniqueness) of solutions for matrix dynamic equations.

Extended previous theories to systems of n^2 matrices.

Identified suitable Lipschitz conditions for generalized n^2-models.

Abstract

In this paper we establish the non--multiplicity of solutions to first order matrix dynamic equations on time scales. The new results verify and extend the notions developed in \cite{thesis} to more complex systems of $n^2$ matrices with the help of ideas developed in \cite[Chap 5]{BP}, identifying Lipschitz conditions suitable to generalised $n^2$--models on time scales.