Theorems of B\^ocher's type for dynamic equations on time scales

TL;DR

This paper establishes conditions under which solutions of systems of dynamic equations on time scales approach finite limits as time tends to infinity, unifying continuous and discrete cases.

Contribution

It introduces new theorems that characterize the asymptotic behavior of solutions to dynamic equations on time scales, extending classical results.

Findings

Solutions tend to finite limits under specified conditions

Unified approach for continuous and discrete dynamic equations

Provides criteria for stability and convergence

Abstract

The conditions are found that all solutions of a systems dynamic equations on time scales tends to finite limits as $t\to\infty$.