2019
Том 71
№ 11

All Issues

Trofimchuk E. P.

Articles: 5
Article (Ukrainian)

On the existence and stability of periodic and almost periodic solutions of quasilinear equations with maxima

Bantsur N. R., Trofimchuk E. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 6. - pp. 747–754

We study the problem of existence of periodic and almost periodic solutions of the scalar equation x′ (t) = − δx(t) + pmax u∈[th, t] x(u) + f(t) where δ, pR, with a periodic (almost periodic) perturbation f(t). For these solutions, we establish conditions of global exponential stability and prove uniqueness theorems.

Brief Communications (Russian)

A. M. Samoilenko's numerical-analytic method without determining equation

Kovalenko O. V., Trofimchuk E. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 1. - pp. 138-140

We suggest a modification of A. M. Samoilenko's numerical-analytic method for investigating the problem $dx/dt=f(t,x), \mathfrak{L}(x) = d$ (here $\mathfrak{L}(x): C([0, T], R^n) \rightarrow R^n$ is a linear continuous operator} in which it is not necessary to solve an additional determining equation.

Article (Russian)

On regularity of linear systems with a degenerate matrix by the derivative

Symокоп V. G., Trofimchuk E. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 2. - pp. 279–286

New sufficient conditions for the existence of invariant manifolds are proved for linear systems with degenerate matrix by the derivative.

Article (Ukrainian)

Impulse systems with fixed moments of shocks of general position: The structure of the set of moments of the shocks

Trofimchuk E. P., Trofimchuk S. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 3. - pp. 378–383

Article (Ukrainian)

Impulse systems with fixed shock times of general disposition: Existence, uniqueness of solution, and the well-posedness of the Cauchy problem

Trofimchuk E. P., Trofimchuk S. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 2. - pp. 230–237