2017
Том 69
№ 9

All Issues

Pelyukh G. P.

Articles: 16
Anniversaries (Ukrainian)

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.

Full text (.pdf)

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

Article (Russian)

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

Pelyukh G. P.

↓ Abstract   |   Full text (.pdf)

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 $t = +\infty$.

Article (Russian)

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

Pelyukh G. P.

↓ Abstract   |   Full text (.pdf)

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).

Article (Russian)

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

Pelyukh G. P.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

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

Belskii D. V., Pelyukh G. P.

↓ Abstract   |   Full text (.pdf)

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 = + ∞$.

Article (Russian)

On the Existence of Periodic Solutions of Nonlinear Difference Equations

Pelyukh G. P.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Ukrainian)

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

Pelyukh G. P.

↓ Abstract   |   Full text (.pdf)

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 tR.

Brief Communications (Ukrainian)

Asymptotic Behavior of Solutions of Nonlinear Difference Equations with Continuous Argument

Pelyukh G. P.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

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

Pelyukh G. P.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Structure of a general solution of systems of nonlinear difference equations

Pelyukh G. P.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

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

Pelyukh G. P.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

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

Pelyukh G. P., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Study of a class of systems of nonlinear functional equations

Pelyukh G. P.

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

Article (Ukrainian)

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

Pelyukh G. P.

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

Article (Ukrainian)

Systems of nonlinear functional equations with singularities

Pelyukh G. P.

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

Article (Ukrainian)

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

Pelyukh G. P.

Full text (.pdf)

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