Komarnyts'ka L. I.
Dirichlet-Type Problems for Systems of Partial Differential Equations Unresolved with Respect to the Highest Time Derivative
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.
Boundary-value problems for differential equations unsolvable with respect to the higher time derivative
Ukr. Mat. Zh. - 1995. - 47, № 9. - pp. 1197–1208
For differential equations with constant coefficients unsolvable with respect to the higher time derivative, we establish conditions of the existence and uniqueness of solutions of problems with conditions local in time and periodic in space variables. We prove a metric theorem on lower bounds of small denominators appearing in the construction of solutions of the problems.