Il'kiv V. S.
Nonlocal boundary-value problem for a second-order partial differential equation in an unbounded strip
Ukr. Mat. Zh. - 2018. - 70, № 10. - pp. 1374-1381
The conditions of well-posedness of a nonlocal boundary-value problem are established for a second-order linear partial differential equation in an unbounded strip in the case where the real parts of the roots of its characteristic equation are different and nonzero.
Solvability of the Nonlocal Boundary-Value Problem for a System of Differential-Operator Equations in the Sobolev Scale of Spaces and in a Refined Scale
Ukr. Mat. Zh. - 2015. - 67, № 5. - pp. 611-624
We study the solvability of the nonlocal boundary-value problem with one parameter for a system of differential-operator equations in the Sobolev scale of spaces of functions of many complex variables and in the scale of Hörmander spaces which form a refined Sobolev scale. By using the metric approach, we prove the theorems on lower estimates of small denominators appearing in the construction of solutions of the analyzed problem. They imply the unique solvability of the problem for almost all vectors formed by the coefficients of the equation and the parameter of nonlocal conditions.
Problems for partial differential equations with nonlocal conditions. Metric approach to the problem of small denominators
Ukr. Mat. Zh. - 2006. - 58, № 12. - pp. 1624–1650
A survey of works of the authors and their disciples devoted to the investigation of problems with nonlocal conditions with respect to a selected variable in cylindrical domains is presented. These problems are considered for linear equations and systems of partial differential equations that, in general, are ill posed in the Hadamard sense and whose solvability in certain scales of functional spaces is established for almost all (with respect to Lebesgue measure) vectors composed of the coefficients of the problem and the parameters of the domain.
A problem with formal initial conditions for differential equations with constant pseudodifferential coefficients
Ukr. Mat. Zh. - 1998. - 50, № 7. - pp. 877–888
We establish conditions for the unique existence of a solution of a problem with formal initial conditions. We investigate the problem of its solvability in the case where a solution is not unique.
Representation and investigation of solutions of a nonlocal boundary-value problem for a system of partial differential equations
Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 184-194
We study the boundary-value problem for a system of partial differential equations with constant coefficients with conditions nonlocal in time. By using a metric approach, we prove the well-posedness of the problem in the scale of Sobolev spaces of functions periodic in space variables. By using matrix calculus, we construct an explicit representation of a solution.
Ukr. Mat. Zh. - 1986. - 38, № 5. - pp. 582–587
Ukr. Mat. Zh. - 1983. - 35, № 4. - pp. 498—502