2018
Том 70
№ 8

All Issues

Stavroulakis I. P.

Articles: 3
Article (English)

Asymptotic behavior of higher-order neutral difference equations with general arguments

Chatzarakis G. E., Khatibzadeh H., Miliaras G. N., Stavroulakis I. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 3. - pp. 430-450

We study the asymptotic behavior of solutions of the higher-order neutral difference equation $$Δm[x(n)+cx(τ(n))]+p(n)x(σ(n))=0,N∍m≥2,n≥0,$$ where $τ (n)$ is a general retarded argument, $σ(n)$ is a general deviated argument, $c ∈ R; (p(n)) n ≥ 0$ is a sequence of real numbers, $∆$ denotes the forward difference operator $∆x(n) = x(n+1) - x(n)$; and $∆^j$ denotes the jth forward difference operator $∆^j (x(n) = ∆ (∆^{j-1}(x(n)))$ for $j = 2, 3,…,m$. Examples illustrating the results are also given.

Article (English)

Stability analysis with respect to two measures of impulsive systems under structural perturbations

Martynyuk A. A., Stavroulakis I. P.

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Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1476–1484

The asymptotic stability with respect to two measures of impulsive systems under structural perturbations is investigated. Conditions of asymptotic (ρ0, ρ)-stability of the system in terms of the fixed signs of some special matrices are established.

Article (English)

Stability analysis of linear impulsive differential systems under structural perturbation

Martynyuk A. A., Stavroulakis I. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 6. - pp. 784–795

The stability and asymptotic stability of solutions of large-scale linear impulsive systems under structural perturbations are investigated. Sufficient conditions for stability and instability are formulated in terms of the fixed signs of special matrices.