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