Relative asymptotic equivalence of dynamic equations on time scales

Cosme Duque, Hugo Leiva, Abdessamad Tridane

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


This paper aims to study the relative equivalence of the solutions of the following dynamic equations yΔ(t) = A(t) y(t) and xΔ(t) = A(t) x(t) + f(t, x(t)) in the sense that if y(t) is a given solution of the unperturbed system, we provide sufficient conditions to prove that there exists a family of solutions x(t) for the perturbed system such that ∥ y(t) − x(t) ∥ = o(∥ y(t) ∥) , as t→ ∞ , and conversely, given a solution x(t) of the perturbed system, we give sufficient conditions for the existence of a family of solutions y(t) for the unperturbed system, and such that ∥ y(t) − x(t) ∥ = o(∥ x(t) ∥) , as t→ ∞ ; and in doing so, we have to extend Rodrigues inequality, the Lyapunov exponents, and the polynomial exponential trichotomy on time scales.

Original languageEnglish
Article number4
JournalAdvances in Continuous and Discrete Models
Issue number1
Publication statusPublished - Dec 2022


  • Contraction mapping theorem
  • Dynamic equations on time scales
  • Lyapunov exponent
  • Polynomial exponential trichotomy
  • Relative asymptotic equivalence
  • Rodrigues inequality

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Applied Mathematics


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