2019
Том 71
№ 2

All Issues

Hrod I. M.

Articles: 4
Brief Communications (Ukrainian)

Relationship Between the Green and Lyapunov Functions in Linear Extensions of Dynamical Systems

Hrod I. M., Kulik V. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 4. - pp. 551–557

We study systems of linear extensions for dynamical systems. As a result, we establish the relationship between the design matrices in the structure of Green functions and alternating Lyapunov functions.

Article (Ukrainian)

Conditions for the existence of bounded solutions of one class of nonlinear differential equations

Hrod I. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 3. - pp. 317–325

For systems of nonlinear differential equations (dx/dt) = A(x)x + f(t) in a Banach space, we establish sufficient conditions for the existence of their solutions bounded on the entire real axis R.

Article (Ukrainian)

On local perturbations of linear extensions of dynamical systems on a torus

Hrod I. M., Kulik V. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 2. - pp. 282-287

We investigate the problem of preservation of regularity of linear extensions of dynamic systems on a torus under perturbations.

Brief Communications (Ukrainian)

On the smoothness of bounded invariant manifolds of linear inhomogeneous extensions of dynamical systems

Hrod I. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 1. - pp. 136-139

We establish sufficient conditions for the existence of smooth bounded invariant manifolds of dynamical systems.