2019
Том 71
№ 6

All Issues

Klyus I. S.

Articles: 3
Article (Ukrainian)

A Multipoint Problem for Pseudodifferential Equations

Klyus I. S., Ptashnik B. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 1. - pp. 22-29

We investigate the well-posedness of a problem with multipoint conditions with respect to a chosen variable t and periodic conditions with respect to coordinates x 1,...,x p for equations unsolved with respect to the leading derivative with respect to t and containing pseudodifferential operators. We establish conditions for the unique solvability of this problem and prove metric assertions related to lower bounds for small denominators appearing in the course of its solution.

Article (Ukrainian)

A multipoint problem for partial differential equations unresolved with respect to the higher time derivative

Klyus I. S., Ptashnik B. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 12. - pp. 1604–1613

We investigate the well-posedness of problems for partial differential equations unresolved with respect to the higher time derivative with multipoint conditions with respect to time. By using the metric approach, we determine lower bounds for small denominators appearing in the course of the solution of the problems.

Article (Ukrainian)

Multipoint problem for hyperbolic equations with variable coefficients

Klyus I. S., Ptashnik B. I., Vasylyshyn P. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 11. - pp. 1468-1476

By using the metric approach, we study the problem of classical well-posedness of a problem with multipoint conditions with respect to time in a tube domain for linear hyperbolic equations of order 2n (n ≥ 1) with coefficients depending onx. We prove metric theorems on lower bounds for small denominators appearing in the course of the solution of the problem.