Vlasii O. D.
Nonlocal boundary-value problem for linear partial differential equations unsolved with respect to the higher time derivative
Ukr. Mat. Zh. - 2007. - 59, № 3. - pp. 370–381
We study the well-posedness of the problem with general nonlocal boundary conditions in the time variable and conditions of periodicity in the space coordinates for partial differential equations unsolved with respect to the higher time derivative. We establish the conditions of existence and uniqueness of the solution of the considered problem. In the proof of existence of the solution, we use the method of divided differences. We also prove metric statements on the lower bounds of small denominators appearing in constructing the solution of the problem.
A Problem with Nonlocal Conditions for Partial Differential Equations Unsolved with Respect to the Leading Derivative
Ukr. Mat. Zh. - 2003. - 55, № 8. - pp. 1022-1034
In the domain that is the product of a segment and a p-dimensional torus, we investigate the well-posedness of a problem with nonlocal boundary conditions for a partial differential equation unsolved with respect to the leading derivative with respect to a selected variable. We establish conditions for the the classical well-posedness of the problem and prove metric theorems on the lower bounds of small denominators appearing in the course of its solution.
Ukr. Mat. Zh. - 2001. - 53, № 10. - pp. 1328-1336
We establish conditions for the unique solvability of a problem for partial differential equations with coefficients dependent on variables t and x in a rectangular domain with nonlocal two-point conditions with respect to t and local boundary conditions with respect to x. We prove metric statements related to lower bounds of small denominators appearing in the course of solution of the problem.