2019
Том 71
№ 8

All Issues

Vu Tuan

Articles: 5
Article (English)

Asymptotic Equivalence of Triangular Differential Equations in Hilbert Spaces

Dang Dinh Chau, Vu Tuan

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 3. - pp. 329–337

In this article, we study conditions for the asymptotic equivalence of differential equations in Hilbert spaces. We also discuss the relationship between the properties of solutions of differential equations of triangular form and those of truncated differential equations.

Brief Communications (English)

Some Results on Asymptotic Stability of Order α

Vu Thi Thu Huong, Vu Tuan

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 2. - pp. 250–257

Quasi-equiasymptotic stability of order $α (α ∈ ℝ_{+} * )$ with respect to a part of variables is considered. Some sufficient conditions, a converse theorem, and a theorem on multistability are proved.

Brief Communications (English)

On the Asymptotic Behavior of Solutions of Differential Systems

Pham Van Viet, Vu Tuan

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 1. - pp. 137–142

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 $M\frac{{\varphi (t_0 )}}{{\varphi (t)}}$.

Article (Ukrainian)

Stability of Solutions of a Quasilinear Index-2 Tractable Differential Algebraic Equation by the Lyapunov Second Method

Pham Van Viet, Vu Tuan

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 10. - pp. 1321-1334

The Lyapunov second method is an important tool in the qualitative theory of ordinary differential equations. In this paper, we consider the behavior of solutions of quasilinear index-2 tractable differential algebraic equations. Using the Lyapunov second method, we prove sufficient conditions for the stability of zero solution of such equations.

Brief Communications (Russian)

On the operational theory of I. Z. Shtokalo in the solution of linear differential equations

Vu Tuan

Full text (.pdf)

Ukr. Mat. Zh. - 1963. - 15, № 3. - pp. 303-305