2019
Том 71
№ 1

All Issues

Slyusarchuk V. E.

Articles: 15
Article (Russian)

General Theorems on the Existence and Uniqueness of Solutions of Impulsive Differential Equations

Slyusarchuk V. E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 954-964

We study the Cauchy problem for impulsive differential equations in the general case.

Article (Russian)

Essentially unstable solutions of difference equations

Slyusarchuk V. E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 12. - pp. 1659–1672

We study the essential instability of solutions of linear and nonlinear difference equations.

Article (Russian)

Necessary and sufficient conditions for the oscillation of solutions of nonlinear differential equations with pulse influence in a banach space

Slyusarchuk V. E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 1. - pp. 98–109

We obtain necessary and sufficient conditions for the oscillation of solutions of nonlinear second-order differential equations with pulse influence in a Banach space.

Article (Russian)

Nonlinear differential equations with asymptotically stable solutions

Slyusarchuk V. E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 2. - pp. 264–273

We establish conditions of asymptotic stability of all solutions of the equation \(\frac{{dx}}{{dt}} = A(x)x\) , t≥0in a Banach space E in the case where σ(A(x)⊂{λ:Reλ<0}∀xE. We give an example of an equation with unstable solutions.

Article (Russian)

Investigation of a nonlinear difference equation in a Banach space in a neighborhood of a quasiperiodic solution

Samoilenko A. M., Slyusarchuk V. E., Slyusarchuk V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1661–1676

We investigate the behavior of a diserete dynamical system in a neighborhood of a quasiperiodic trajeetory for the case of an infinite-dimensional Banach space We find conditions sufficient for the system considered to reduce, in such a neighborhood, to a system with quasiperiodic coefficients.

Article (Russian)

Nonlinear difference equations with asymptotically stable solutions

Slyusarchuk V. E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 7. - pp. 970–980. July

We establish conditions of asymptotic stability for all solutions of the equation X n+1=F(X n ), n≥0, in the Banach space E in the case where r(F′(x))<1 ∀ x ∈ E, r′(x) is the spectral radius of F′(x). An example of an equation with an unstable solution is given.

Article (Russian)

Refinement of Kneser theorem on zeros of solutions of the equation $y" + p(x)y = 0$

Slyusarchuk V. E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 4. - pp. 520-524

We find conditions for a linear homogeneous second order equation to be nonoscfflatory on the half-axis and such that its solutions have infinitely many zeros.

Article (Ukrainian)

Exponential dichotomy of solutions of impulse systems

Slyusarchuk V. E.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 6. - pp. 779-783

Article (Ukrainian)

Weakly nonlinear perturbations of normally solvable functional-differential and discrete equations

Slyusarchuk V. E.

Full text (.pdf)

Ukr. Mat. Zh. - 1987. - 39, № 5. - pp. 660–662

Article (Ukrainian)

Representation of the bounded solutions of discrete linear system

Slyusarchuk V. E.

Full text (.pdf)

Ukr. Mat. Zh. - 1987. - 39, № 2. - pp. 210-215

Article (Ukrainian)

Exponential dichotomy for solutions of discrete systems

Slyusarchuk V. E.

Full text (.pdf)

Ukr. Mat. Zh. - 1983. - 35, № 1. - pp. 108—115

Article (Ukrainian)

A statement about instability in the first approximation

Slyusarchuk V. E.

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Ukr. Mat. Zh. - 1982. - 34, № 2. - pp. 241-244

Article (Ukrainian)

Invertibility of almost-periodic operators generated by discrete systems

Slyusarchuk V. E.

Full text (.pdf)

Ukr. Mat. Zh. - 1979. - 31, № 4. - pp. 460–463

Article (Ukrainian)

Solution of linear functional equations in space of functions, bounded in R n

Slyusarchuk V. E.

Full text (.pdf)

Ukr. Mat. Zh. - 1978. - 30, № 3. - pp. 416–422

Article (Ukrainian)

On the stability of solutions of linear functional—Differential equations with random perturbations of the parameters

Slyusarchuk V. E., Yasinskii E. F., Yasinsky V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1973. - 25, № 3. - pp. 409—415