2019
Том 71
№ 1

Kulik V. L.

Articles: 29
Article (Ukrainian)

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

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

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

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

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

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

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

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)

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

Article (Ukrainian)

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

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)

Regular linear extensions of dynamical systems on a torus

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

Article (Ukrainian)

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

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

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

Article (Ukrainian)

Bounded solutions of systems of linear differential equations

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

Article (Ukrainian)

The alternating lyapunov functions and preservation of invariant tori under perturbations

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

Article (Ukrainian)

Lyapunov functions and bounded solutions of linear systems of differential equations

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

Article (Ukrainian)

Weakly regular linear systems of differential equations

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

Article (Ukrainian)

Application of quadratic forms in the theory of invariant manifolds

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

Article (Ukrainian)

Bounded solutions of nonlinear systems of differential equations

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

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

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

Article (Ukrainian)

Decomposability of linearized systems of differential equations

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

Article (Ukrainian)

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

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

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

Article (Ukrainian)

Continuity of Green's function for the invariant torus problem

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

Article (Ukrainian)

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

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

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

Article (Ukrainian)

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

Article (Ukrainian)

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

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

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