2019
Том 71
№ 11

# Slyusarchuk V. E.

Articles: 16
Article (Russian)

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

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

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

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

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

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

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)

### Theorems on instability of systems with respect to linear approximation

Ukr. Mat. Zh. - 1996. - 48, № 8. - pp. 1104-1113

We study the problem of instability of solutions of differential equations with a stationary linear part and a nonstationary nonlinear compact part in a Banach space.

Article (Russian)

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

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

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

Article (Ukrainian)

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

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

Article (Ukrainian)

### Representation of the bounded solutions of discrete linear system

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

Article (Ukrainian)

### Exponential dichotomy for solutions of discrete systems

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

Article (Ukrainian)

### A statement about instability in the first approximation

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

Article (Ukrainian)

### Invertibility of almost-periodic operators generated by discrete systems

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

Article (Ukrainian)

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

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

Article (Ukrainian)

### On the stability of solutions of linear functionalвЂ”Differential equations with random perturbations of the parameters

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