2019
Том 71
№ 2

# Perestyuk N. A.

Articles: 53
Article (Russian)

### Averaging of fuzzy systems

Ukr. Mat. Zh. - 2018. - 70, № 3. - pp. 412-428

We develop the ideas of the method of averaging for some classes of fuzzy systems (fuzzy differential equations with delay, fuzzy differential equations with pulsed action, fuzzy integral equations, fuzzy differential inclusions and differential inclusions with fuzzy right-hand sides without and with pulsed action).

Anniversaries (Ukrainian)

### Anatolii Mykhailovych Samoilenko (on his 80th birthday)

Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 3-6

Article (Ukrainian)

### Stability of global attractors of impulsive infinite-dimensional systems

Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 29-39

The stability of global attractor is proved for an impulsive infinite-dimensional dynamical system. The obtained abstract results are applied to a weakly nonlinear parabolic equation whose solutions are subjected to impulsive perturbations at the times of intersection with a certain surface of the phase space.

Anniversaries (Ukrainian)

### On the 100th birthday of outstanding mathematician and mechanic Yurii Oleksiiovych Mytropol’s’kyi (03.01.1917 – 14.06.2008)

Ukr. Mat. Zh. - 2017. - 69, № 1. - pp. 132-144

Anniversaries (Ukrainian)

### Volodymyr Leonidovych Makarov (on his 75th birthday)

Ukr. Mat. Zh. - 2016. - 68, № 12. - pp. 1715-1717

Article (Russian)

### Global attractors of impulsive infinite-dimensional systems

Ukr. Mat. Zh. - 2016. - 68, № 4. - pp. 517-528

We study the existence of global attractors in discontinuous infinite-dimensional dynamical systems, which may have trajectories with infinitely many impulsive perturbations. We also select a class of impulsive systems for which the existence of a global attractor is proved for weakly nonlinear parabolic equations.

Article (Ukrainian)

### On Preservation of the Invariant torus for Multifrequency Systems

Ukr. Mat. Zh. - 2013. - 65, № 11. - pp. 1498–1505

We establish new conditions for the preservation of an asymptotically stable invariant toroidal manifold of the linear extension of a dynamical system on a torus under small perturbations in a set of nonwandering points. The proposed approach is applied to the investigation of the existence and stability of the invariant tori of linear extensions of the dynamical systems with simple structures of limit sets and recurrent trajectories.

Anniversaries (Ukrainian)

### Anatolii Mykhailovych Samoilenko (on his 75th birthday)

Ukr. Mat. Zh. - 2013. - 65, № 1. - pp. 3 - 6

Article (Russian)

### Averaging of set-valued impulsive systems

Ukr. Mat. Zh. - 2013. - 65, № 1. - pp. 126-142

We give a review of the development of ideas of the averaging method for some classes of set-valued impulsive systems (impulsive differential inclusions, impulsive differential equations and inclusions with Hukuhara derivative, and impulsive fuzzy differential equations and inclusions).

Anniversaries (Ukrainian)

### Mykola Ivanovych Shkil' (on his 80th birthday)

Ukr. Mat. Zh. - 2012. - 64, № 12. - pp. 1720-1722

Anniversaries (Ukrainian)

### Dmytro Ivanovych Martynyuk (on the 70th anniversary of his birthday)

Ukr. Mat. Zh. - 2012. - 64, № 4. - pp. 571-573

Article (Ukrainian)

### Green–Samoilenko operator in the theory of invariant sets of nonlinear differential equations

Ukr. Mat. Zh. - 2009. - 61, № 7. - pp. 948-957

We establish conditions for the existence of an invariant set of the system of differential equations $$\frac{dφ}{dt} = a(φ),\quad \frac{dx}{dt} = P(φ)x + F(φ,x),$$ where $a: Φ → Φ, P: Φ → L(X, X)$, and $F: Φ × X→X$ are continuous mappings and $Φ$ and $X$ are finite-dimensional Banach spaces.

Anniversaries (Ukrainian)

### Fifty years devoted to science (on the 70th birthday of Anatolii Mykhailovych Samoilenko)

Ukr. Mat. Zh. - 2008. - 60, № 1. - pp. 3–7

Article (Ukrainian)

### Some modern aspects of the theory of impulsive differential equations

Ukr. Mat. Zh. - 2008. - 60, № 1. - pp. 81–94

We give a brief survey of the main results obtained in recent years in the theory of impulsive differential equations.

Anniversaries (Ukrainian)

### On the 90th birthday of Yurii Alekseevich Mitropol’skii

Ukr. Mat. Zh. - 2007. - 59, № 2. - pp. 147–151

Article (Ukrainian)

### Once again on the Samoilenko numerical-analytic method of successive periodic approximations

Ukr. Mat. Zh. - 2006. - 58, № 4. - pp. 472–488

A new numerical-analytic algorithm for the investigation of periodic solutions of nonlinear periodic systems of differential equations dx/dt = A(t) x+ ƒ(t, x) in the critical case is developed. The problem of the existence of solutions and their approximate construction is studied. Estimates for the convergence of successive periodic approximations are obtained.

Article (Russian)

### On the Solvability of Impulsive Differential-Algebraic Equations

Ukr. Mat. Zh. - 2005. - 57, № 4. - pp. 458–468

We establish theorems on the existence and uniqueness of a solution of the impulsive differential-algebraic equation $$\frac{d}{{dt}}[Au(t)] + Bu(t) = f(t,u(t)),$$ where the matrix A may be singular. The results are applied to the theory of electric circuits.

Article (Russian)

### Global Attractor of an Evolution Inclusion with Pulse Influence at Fixed Moments of Time

Ukr. Mat. Zh. - 2003. - 55, № 8. - pp. 1058-1068

We consider an autonomous evolution inclusion with pulse perturbations at fixed moments of time. Under the conditions of global solvability, we prove the existence of a minimal compact set in the phase space that attracts all trajectories.

Article (Ukrainian)

### Conditions for the Existence of Nonoscillating Solutions of Nonlinear Differential Equations with Delay and Pulse Influence in a Banach Space

Ukr. Mat. Zh. - 2003. - 55, № 6. - pp. 790-798

For nonlinear differential second-order equations with delay and pulse influence in a Banach space, we establish necessary and sufficient conditions for the existence of their solutions nonoscillating with respect to a subspace.

Article (Ukrainian)

### International Scientific Conference on the Theory of Evolution Equations (Fifth Bogolyubov Readings)

Ukr. Mat. Zh. - 2002. - 54, № 10. - pp. 1440

Anniversaries (Ukrainian)

### Mykhailo Iosypovych Yadrenko (On His 70th Birthday)

Ukr. Mat. Zh. - 2002. - 54, № 4. - pp. 435-438

Anniversaries (Ukrainian)

### Dmytro Ivanovych Martynyuk (On the 60th Anniversary of His Birth)

Ukr. Mat. Zh. - 2002. - 54, № 3. - pp. 291-292

Article (Ukrainian)

### On Stability of Integral Sets of Impulsive Differential Systems

Ukr. Mat. Zh. - 2002. - 54, № 2. - pp. 249-257

We introduce the notion of stability of integral sets of impulsive differential systems of general form (with nonfixed times of impulse influence). We establish conditions sufficient for the stability of an integral set.

Article (Russian)

### On the Existence of Periodic Solutions for Certain Classes of Systems of Differential Equations with Random Pulse Influence

Ukr. Mat. Zh. - 2001. - 53, № 8. - pp. 1061-1079

We establish conditions for the existence of periodic solutions for systems of differential equations with random right-hand side and random pulse influence at fixed times. We consider the case of small pulse perturbation and weakly nonlinear systems.

Article (Ukrainian)

### On the Stability of Invariant Sets of Discontinuous Dynamical Systems

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 78-84

We establish sufficient conditions for the stability, asymptotic stability, and instability of invariant sets of discontinuous dynamical systems.

Article (Russian)

### Controlled Pulse Influence in Games with Fixed Termination Time

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1112-1118

We construct optimal strategies for players and determine the sets of initial positions favorable for one player or another.

Article (Ukrainian)

### On the stability of a trivial invariant torus of one class of impulsive systems

Ukr. Mat. Zh. - 1998. - 50, № 3. - pp. 338–349

We consider the problem of asymptotic stability of the trivial invariant torus of one class of impulsive systems. Sufficient criteria of asymptotic stability are obtained by the method of freezing in one case, and by the direct Lyapunov method for the investigation of stability of solutions of impulsive systems in another case.

Anniversaries (Ukrainian)

### Anatolii Mikhailovich Samoilenko (on his 60th birthday)

Ukr. Mat. Zh. - 1998. - 50, № 1. - pp. 3–4

Article (Ukrainian)

### On the stability of an invariant torus

Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1212-1222

We consider the problem of the asymptotic stability for trivial invariant torus of a linear extension of dynamical system on a torus. We formulate and prove sufficient criteria of asymptotic stability and study conditions for the existence and uniqueness of the Lyapunov functions of fixed sign.

Brief Communications (Ukrainian)

### On the existence of discontinuous limit cycles for one system of differential equations with pulse influence

Ukr. Mat. Zh. - 1997. - 49, № 8. - pp. 1127–1134

For one system of differential equations with pulse influence, we establish conditions under which a positive root of the equation for stationary amplitudes obtained from equations of the first approximation generates a discontinuous limit cycle. We construct improved first approximations for the system under consideration.

Brief Communications (Russian)

### Periodic solutions of a weakly nonlinear system of partial differential equations with pulse influence

Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 601–605

We establish conditions of the existence of solutions periodic in t with period T for a weakly nonlinear system of partial differential equations with pulse influence.

Article (Russian)

### Stability of solutions of pulsed systems

Ukr. Mat. Zh. - 1997. - 49, № 1. - pp. 98–111

We present the principal results in the theory of stability of pulse differential equations obtained by mathematicians of the Kiev scientific school of nonlinear mechanics. We also present some results of foreign authors.

Article (Ukrainian)

### Reducibility of nonlinear almost periodic systems of difference equations on an infinite-dimensional torus

Ukr. Mat. Zh. - 1994. - 46, № 9. - pp. 1216–1223

Article (Ukrainian)

### Green-Samoilenko function and existence of integral sets of linear extensions of nonautonomous equations

Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1067–1071

An integral invariant set is constructed for systems of differential equations by using the Green-Samoilenko function. The problem of asymptotic stability of this set is studied.

Article (Ukrainian)

### Reducibility of nonlinear almost periodic systems of difference equations given on a torus

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 404–412

We establish sufficient conditions for a nonlinear system of difference equations x(t + 1) =x(t) + ? + P(x(t),t)+ ? to be reducible to the system y(t + 1) =y(t) + ?. Here, P(x, t) is a function 2?-periodic in xi(i = 1, ...,n) and almost periodic int with a frequency basis ?.

Article (Ukrainian)

### Integral sets of systems of difference equations

Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1613–1621

The problem of existence of integral sets of systems of difference equations is studied. We establish sufficient conditions for the existence of these sets and their stability. For the system under consideration, the behavior of trajectories that originate in a sufficiently small neighborhood of integral sets is investigated.

Article (Ukrainian)

### On a comparison method for pulse systems in the space R

Ukr. Mat. Zh. - 1993. - 45, № 6. - pp. 753–762

Article (Ukrainian)

### Asymptotic representation of solutions of regularly perturbed systems of differential equations with nonclassical right-hand side

Ukr. Mat. Zh. - 1991. - 43, № 10. - pp. 1298–1304

Article (Ukrainian)

### Method of freezing in systems with impulse action

Ukr. Mat. Zh. - 1991. - 43, № 6. - pp. 848–853

Article (Ukrainian)

### Generalized solutions of impulse systems and the phenomenon of pulsations

Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 657–663

Article (Ukrainian)

### Stability of periodic solutions of differential equations with impulse action on surfaces

Ukr. Mat. Zh. - 1989. - 41, № 12. - pp. 1596–1601

Article (Ukrainian)

### Differentiable dependence of the solutions of impulse systems on initial data

Ukr. Mat. Zh. - 1989. - 41, № 8. - pp. 1028–1033

Article (Ukrainian)

### Almost-periodic solutions of impulse systems

Ukr. Mat. Zh. - 1987. - 39, № 1. - pp. 74-80

Article (Ukrainian)

### Asymptotic integration of weakly nonlinear systems with impulses

Ukr. Mat. Zh. - 1985. - 37, № 3. - pp. 361–363

Article (Ukrainian)

### Averaging method in systems with impulses

Ukr. Mat. Zh. - 1985. - 37, № 1. - pp. 56 – 64

Article (Ukrainian)

### Almost-periodic solutions of one class of systems with impulses

Ukr. Mat. Zh. - 1984. - 36, № 4. - pp. 486 – 490

Article (Ukrainian)

### A contribution to the stability problem for solutions of systems of differential equations with impulses

Ukr. Mat. Zh. - 1984. - 36, № 2. - pp. 190 - 195

Article (Ukrainian)

### Invariant sets of a class of discontinuous dynamical systems

Ukr. Mat. Zh. - 1984. - 36, № 1. - pp. 63 - 68

Article (Ukrainian)

### Periodic and almost-periodic solutions of impulsive differential equations

Ukr. Mat. Zh. - 1982. - 34, № 1. - pp. 66-73

Article (Ukrainian)

### Periodic solutions of nonlinear differential equations with impulsive action

Ukr. Mat. Zh. - 1979. - 31, № 5. - pp. 517–524

Article (Ukrainian)

### The problem of justifying the averaging method for second-order equations with impulsive action

Ukr. Mat. Zh. - 1977. - 29, № 6. - pp. 750–762

Article (Ukrainian)

### The method of averaging in systems with an impulsive action

Ukr. Mat. Zh. - 1974. - 26, № 3. - pp. 411–418

Article (Ukrainian)

### Invariant sets of systems with instantaneous changes in standard form

Ukr. Mat. Zh. - 1973. - 25, № 1. - pp. 129-134