2019
Том 71
№ 8

All Issues

Bilusyak N.I.

Articles: 3
Article (Ukrainian)

Dirichlet-Type Problems for Systems of Partial Differential Equations Unresolved with Respect to the Highest Time Derivative

Bilusyak N.I., Komarnyts'ka L. I., Ptashnik B. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 12. - pp. 1592-1602

We establish conditions for the correct solvability of problems for systems of partial differential equations unresolved with respect to the highest time derivative with Dirichlet-type conditions with respect to time and periodic conditions with respect to space variables. We prove metric theorems on lower bounds for small denominators appearing in the course of the solution of these problems.

Brief Communications (Ukrainian)

Boundary-Value Problem for Weakly Nonlinear Hyperbolic Equations with Variable Coefficients

Bilusyak N.I., Ptashnik B. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 9. - pp. 1281-1286

We establish conditions for the unique solvability of a boundary-value problem for a weakly nonlinear hyperbolic equation of order 2n, n > (3p + 1)/2, with coefficients dependent on the space coordinates and data given on the entire boundary of a cylindric domain \(D \subset \mathbb{R}^{p + 1}\) . The investigation of this problem is connected with the problem of small denominators.

Brief Communications (Ukrainian)

A Boundary-Value Problem for Weakly Nonlinear Hyperbolic Equations with Data on the Entire Boundary of a Domain

Bilusyak N.I., Ptashnik B. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 2. - pp. 244-249

In a domain that is the Cartesian product of a segment and a p-dimensional torus, we investigate a boundary-value problem for weakly nonlinear hyperbolic equations of higher order. For almost all (with respect to Lebesgue measure) parameters of the domain, we establish conditions for the existence of a unique solution of the problem.