Global attractivity of nonlinear delay dynamic equations on time scales via Lyapunov functional method
Mathematica Slovaca, vol.75, no.3, pp.619-632, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 75 Issue: 3
- Publication Date: 2025
- Doi Number: 10.1515/ms-2025-0045
- Journal Name: Mathematica Slovaca
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Page Numbers: pp.619-632
- Keywords: Lyapunov's functional method, globally attracting, nonlinear delay dynamic equation
- Dokuz Eylül University Affiliated: Yes
Abstract
In this paper, we consider the nonlinear dynamic equation with variable delay yΔ(t)+F(t,y(τ(t)))=0for t [t0,∞)T, where is a time scale unbounded above, τ is an rd-continuous delay function and F is rd-continuous in its first component and continuous in its second component. We investigate the global attractivity of the trivial solution of (∗) by the well-known Lyapunov's functional method. Our research significantly enhances and expands upon various established results in the literature, presents new results on time scales by defining a new companion function, and offers original perspectives for nonlinear delay dynamic equations on time scales. In addition, we present some illustrative examples on time scales to showcase the applicability of the new results.