# Pelyukh G. P.

### Asyptotic bounds for the solutions of functional and differentialfunctional equations with constant and linear delays

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 9. - pp. 1249-1270

UDC 517.929

We establish asymptotic bounds for the solutions of functional and differential-functional equations with linearly transformed arguments and constant delays.

### Asymptotic estimates for the solutions of a differential-functional equation with linear delay

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 1. - pp. 129-138

We establish new properties of the solutions of a differential-functional equation with linearly transformed argument.

### Oleksandr Mykolaiovych Sharkovs’kyi (on his 80th birthday)

Fedorenko V. V., Ivanov А. F., Khusainov D. Ya., Kolyada S. F., Maistrenko Yu. L., Parasyuk I. O., Pelyukh G. P., Romanenko O. Yu., Samoilenko V. G., Shevchuk I. A., Sivak A. G., Tkachenko V. I., Trofimchuk S. I.

Ukr. Mat. Zh. - 2017. - 69, № 2. - pp. 257-260

### On the asymptotic properties of continuous solutions of the systems of nonlinear functional equations

Ukr. Mat. Zh. - 2013. - 65, № 1. - pp. 119-125

For systems of nonlinear functional equations, we study asymptotic properties of their solutions continuously differentiable and bounded for $t \geq T > 0$ in a neighborhood of the singular point $t = +\infty$.

### On properties of solutions of a limit problem for systems of nonlinear functional differential equations of neutral type

Ukr. Mat. Zh. - 2008. - 60, № 2. - pp. 217–224

For a class of systems of nonlinear differential-functional equations, we study asymptotic characteristics of their solutions continuously differentiable and bounded for
*t* >* T *> 0 (along with the first derivative).

### Investigation of the structure of the set of continuous solutions of systems of nonlinear difference equations with continuous argument

Ukr. Mat. Zh. - 2007. - 59, № 1. - pp. 99–108

We study the structure of the set of continuous solutions for one class of systems of nonlinear difference equations with continuous argument in the neighborhoods of equilibrium states.

### On the behavior of solutions of linear functional differential equations with constant coefficients and linearly transformed argument in neighborhoods of singular points

Ukr. Mat. Zh. - 2005. - 57, № 12. - pp. 1668–1676

We establish new properties of $C^1 (0, + ∞)$-solutions of the linear functional differential equation $\dot{x}(t) = ax(t) + bx(qt) + cx(qt)$ in the neighborhoods of the singular points $t = 0$$ and t = + ∞$.

### On the Existence of Periodic Solutions of Nonlinear Difference Equations

Ukr. Mat. Zh. - 2002. - 54, № 12. - pp. 1626-1633

We obtain new sufficient conditions for the existence and uniqueness of an *N*-periodic solution (*N* is a positive integer) of a nonlinear difference equation with continuous argument of the form *x*(*t* + 1) = *f*(*x*(*t*)) and investigate the properties of this solution.

### On Global Solutions of Systems of Nonlinear Functional Differential Equations with Deviating Argument Dependent on Unknown Functions

Ukr. Mat. Zh. - 2002. - 54, № 3. - pp. 402-407

For a system of nonlinear functional differential equations with nonlinear deviations of an argument, we obtain sufficient conditions for the existence of a continuously differentiable solution bounded for *t* ∈ *R*.

### Asymptotic Behavior of Solutions of Nonlinear Difference Equations with Continuous Argument

Ukr. Mat. Zh. - 2002. - 54, № 1. - pp. 138-141

We establish conditions for the existence and uniqueness of continuous asymptotically periodic solutions of nonlinear difference equations with continuous argument.

### On the Existence of Local Smooth Solutions of Systems of Nonlinear Functional Equations with Deviations Dependent on Unknown Functions

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 64-77

We obtain conditions for the existence of a local differentiable solution of a system of nonlinear functional equations with nonlinear deviations of an argument.

### General Solution of Systems of Nonlinear Difference Equations with Continuous Argument

Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 936-953

We investigate the structure of the general solution of a system of nonlinear difference equations with continuous argument in the neighborhood of an equilibrium state.

### On the existence and uniqueness of solutions continuous and bounded on the real axis for nonlinear functional equations

Ukr. Mat. Zh. - 2000. - 52, № 3. - pp. 416-418

For one class of nonlinear functional equations, we establish conditions for the existence and uniqueness of solutions continuous and bounded on the real axis.

### Structure of a general solution of systems of nonlinear difference equations

Ukr. Mat. Zh. - 1999. - 51, № 10. - pp. 1368–1378

We investigate the structure of a general solution of systems of nonlinear difference equations with continuous argument in a neighborhood of the state of equilibrium.

### Solutions of systems of nonlinear difference equations that are continuous and bounded on the entire real axis and their properties

Ukr. Mat. Zh. - 1998. - 50, № 12. - pp. 1636–1645

For a system of nonlinear difference equations, we establish conditions for the existence and uniqueness of a solution bounded on the entire real axis and study its properties.

### On periodic solutions of nonlinear difference equations in the critical case

Ukr. Mat. Zh. - 1998. - 50, № 2. - pp. 304–308

We establish conditions for the existence and uniqueness of a periodic solution of one nonlinear difference equation.

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

Berezansky Yu. M., Boichuk О. A., Korneichuk N. P., Korolyuk V. S., Koshlyakov V. N., Kulik V. L., Luchka A. Y., Mitropolskiy Yu. A., Pelyukh G. P., Perestyuk N. A., Skorokhod A. V., Skrypnik I. V., Tkachenko V. I., Trofimchuk S. I.

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

### On periodic solutions of difference equations with continuous argument

Ukr. Mat. Zh. - 1996. - 48, № 1. - pp. 140-145

We establish conditions for the existence of periodic solutions of systems of nonlinear difference equations with continuous argument.

### Solutions of systems of nonlinear difference-differential equations of neutral type asymptotically bounded in the entire axis

Pelyukh G. P., Samoilenko A. M.

Ukr. Mat. Zh. - 1994. - 46, № 11. - pp. 1597-1601

For a certain class of systems of difference-differential equations of neutral type, we study the properties of solutions asymptotically bounded on the entire axis.

### On the existence and properties of periodic solutions of discrete difference equations

Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1382–1387

We establish conditions for the existence of periodic solutions for a broad class of nonlinear difference equations with discrete argument.

### Solutions of systems of nonlinear functional-differential equations bounded in the entire real axis and their properties

Pelyukh G. P., Samoilenko A. M.

Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 737–747

For a system of nonlinear functional-differential equations with a linearly transformed argument, we establish the existence and uniqueness conditions for a solution bounded in the entire real axis and study the properties of this solution.

### Study of a class of systems of nonlinear functional equations

Ukr. Mat. Zh. - 1986. - 38, № 2. - pp. 261–265

### General solution of systems of nonlinear functional equations in neighborhoods of singularities

Ukr. Mat. Zh. - 1983. - 35, № 4. - pp. 516—519

### Systems of nonlinear functional equations with singularities

Ukr. Mat. Zh. - 1983. - 35, № 2. - pp. 173—181

### Cr-solutions of nonlinear functional equations with many deviations of the argument

Ukr. Mat. Zh. - 1978. - 30, № 1. - pp. 79–85