On the Asymptotic Behavior of Solutions of Differential Systems

  • Van Viet Pham
  • Tuan Vu


There are many studies on the asymptotic behavior of solutions of differential equations. In the present paper, we consider another aspect of this problem, namely, the rate of the asymptotic convergence of solutions. Let $ϕ (t)$ be a scalar continuous monotonically increasing positive function tending to ∞ as $t → ∞$. It is established that if all solutions of a differential system satisfy the inequality $$\left\| {x(t;t_0 ,\;x_0 )} \right\| \leqslant M\frac{{\varphi (t_0 )}}{{\varphi (t)}}\quad \operatorname{for} \;all\quad t \geqslant t_0 ,\quad x_0 \in \left\{ {x:\left\| x \right\| \leqslant \alpha } \right\},$$ then the solution $x(t; t_0, x_0)$ of this differential system tends to 0 faster than $M\frac{{\varphi (t_0 )}}{{\varphi (t)}}$.
How to Cite
Pham, V. V., and T. Vu. “On the Asymptotic Behavior of Solutions of Differential Systems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, no. 1, Jan. 2005, pp. 137–142, https://umj.imath.kiev.ua/index.php/umj/article/view/3581.
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