2019
Том 71
№ 11

# Trofimchuk E. P.

Articles: 5
Article (Ukrainian)

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

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

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

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

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

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