2019
Том 71
№ 7

All Issues

Sylyuha L. P.

Articles: 2
Article (Ukrainian)

Multipoint problem for typeless systems of differential equations with constant coefficients

Ptashnik B. I., Sylyuha L. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1236–1249

For typeless systems of differential equations with constant coefficients, we investigate the well-posedness of the problem with multipoint conditions for a selected variable and 2π-periodic conditions for the other coordinates. The conditions of univalent solvability are established and the metric theorems are proved for lower bounds of small denominators that appear in the construction of solutions of the problems.

Article (Russian)

Multipoint problem for typeless factorized differential operators

Ptashnik B. I., Sylyuha L. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 1. - pp. 66-79

We analyze the well-posedness of a problem with multipoint conditions in the time variable and periodic conditions in the spatial coordinates for differential operators decomposable into operators of the first order with complex coefficients. We establish conditions for the existence and uniqueness of the classical solution of the problem under consideration and prove metric theorems for the lower estimates of small denominators appearing in the process of construction of the solution.