2019
Том 71
№ 11

All Issues

Kulik V. L.

Articles: 30
Article (Ukrainian)

Construction of Lyapunov Functions in the Theory of Regular Linear Extensions of Dynamical Systems on a Torus

Kulik V. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 10. - pp. 1358-1365

Lyapunov functions are considered in the form of linear combinations of quadratic forms. We study the conditions under which the linear extensions of dynamic systems on a torus are regular.

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)

Alternating Lyapunov functions in the theory of linear extensions of dynamical systems on a torus

Kulik V. L., Stepanenko N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 4. - pp. 488–500

We consider a series of problems connected with the application of quadratic-form Lyapunov functions to the investigation of the properties of regularity of linear extensions of dynamic systems on a torus.

Article (Ukrainian)

Integral Form of Bounded Solutions of Some Systems of Differential Equations

Kulik V. L., Kulyk H. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 1. - pp. 84–93

We investigate the well-known Gauss variational problem considered over classes of Radon measures associated with a system of sets in a locally compact space. Under fairly general assumptions, we obtain necessary and sufficient conditions for its solvability. As an auxiliary result, we describe potentials of vague and (or) strong limit points of minimizing sequences of measures. The results obtained are also specified for the Newton kernel in $\mathbb{R}^n$.

Brief Communications (Ukrainian)

On Regularity of Certain Linear Expansions of Dynamical Systems on a Torus

Kulik V. L., Stepanenko N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 4. - pp. 568-574

We investigate the problem of the existence of the Green–Samoilenko function for linear expansions of dynamical systems on a torus of the form $$\frac{{d\phi }}{{dt}} = a(\phi ),{\text{ }}C(\phi )\frac{{d\phi }}{{dt}} + \frac{1}{2}\dot C(\phi )x = A(\phi )x,$$ where C(ϕ) ∈ C′(T m; a) is a nondegenerate symmetric matrix.

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.

Article (Russian)

Linear extensions of dynamical systems on a torus that possess Green-Samoilenko functions

Kulik V. L., Wojtowicz B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 2. - pp. 178–188

By using Lyapunov functions with alternating signs, we study problems of regularity and weak regularity for some linear extensions of dynamical systems on a torus.

Anniversaries (Ukrainian)

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.

Full text (.pdf)

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

Article (Ukrainian)

On parameter dependence of bounded invariant manifolds of autonomous systems of differential equations

Bodnarchuk S. V., Kulik V. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 6. - pp. 747-752

We consider bounded invariant manifolds of autonomous systems of differential equations and study the problem of their continuity and continuous differentiability with respect to a parameter.

Article (Ukrainian)

On some classes of regular linear extensions of dynamical systems on a torus

Kulik V. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 11. - pp. 1479–1485

We select some classes of linear extensions of dynamical systems on a torus for which weak regularity implies regularity.

Brief Communications (Russian)

Regular linear extensions of dynamical systems on a torus

Kulik L., Kulik V. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 8. - pp. 1170-1173

We consider certain structures of linear extensions of the dynamical systems on a torus having a single Green's function.

Article (Ukrainian)

Existence of Lyapunov functions of variable sign for linear extensions of dynamical systems on a torus

Kulik V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 12. - pp. 1713–1717

Article (Ukrainian)

Continuity properties of invariant tori and Green's function of linear expansions on a torus

Kulik V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 12. - pp. 1709–1714

Article (Ukrainian)

Bounded solutions of systems of linear differential equations

Kulik V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1987. - 39, № 6. - pp. 727–732

Article (Ukrainian)

The alternating lyapunov functions and preservation of invariant tori under perturbations

Kulik V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1987. - 39, № 1. - pp. 45–52

Article (Ukrainian)

Lyapunov functions and bounded solutions of linear systems of differential equations

Kulik V. L., Mitropolskiy Yu. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 1. - pp. 39–49

Article (Ukrainian)

Weakly regular linear systems of differential equations

Kulik V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1985. - 37, № 4. - pp. 501–506

Article (Ukrainian)

Application of quadratic forms in the theory of invariant manifolds

Kulik V. L., Mitropolskiy Yu. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1985. - 37, № 3. - pp. 306–316

Article (Ukrainian)

Bounded solutions of nonlinear systems of differential equations

Kulik V. L., Mitropolskiy Yu. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1984. - 36, № 6. - pp. 720 – 729

Article (Ukrainian)

Connection between quadratic forms and the Green's function of a linear extension of dynamical systems on the torus

Kulik V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1984. - 36, № 2. - pp. 258 - 262

Article (Ukrainian)

Reversibility of the decomposability theorem of linear extensions of dynamical systems on a torus

Kulik V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1983. - 35, № 1. - pp. 37—41

Article (Ukrainian)

Decomposability of linearized systems of differential equations

Kulik V. L., Samoilenko A. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1982. - 34, № 5. - pp. 587-593

Article (Ukrainian)

Quadratic forms and dichotomy of solutions of systems of linear differential equations

Kulik V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1982. - 34, № 1. - pp. 43-49

Article (Ukrainian)

Quasiperiodic solutions of a linear system of differential equations with a singular matrix in the derivatives

Kulik V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1980. - 32, № 6. - pp. 746–753

Article (Ukrainian)

Continuity of Green's function for the invariant torus problem

Kulik V. L., Samoilenko A. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1978. - 30, № 6. - pp. 779–788

Article (Ukrainian)

Dependence of green's function on a parameter in the invariant torus problem

Kulik V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1978. - 30, № 4. - pp. 545–551

Article (Ukrainian)

Use of asymptotic methods in solving the problem of fluid flow in an elastic pipeline

Krivosheya S. A., Kulik V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1977. - 29, № 1. - pp. 58–66

Article (Ukrainian)

Kulik V. L., Samoilenko A. M.

Ukr. Mat. Zh. - 1975. - 27, № 4. - pp. 

Article (Ukrainian)

On the existence of the Green function of the problem of the invariant torus

Kulik V. L., Samoilenko A. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1975. - 27, № 3. - pp. 348–359

Article (Ukrainian)

On the question of dichotomy for the solutions of systems of linear differential equations

Golets B. I., Kulik V. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1972. - 24, № 4. - pp. 528–531