Pelyukh G. P.

UDC 517.929
We establish asymptotic bounds for the solutions of functional and differential-functional equations with linearly transformed arguments and constant delays.

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

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 $t = +\infty$.

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).

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.

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 = + ∞$.

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.

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.

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

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

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.

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

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.

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.

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

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

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.

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

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.