Akademik Veri Yönetim Sistemi
Mathematica Slovaca, cilt.75, sa.3, ss.619-632, 2025 (SCI-Expanded)
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.