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

Abstract

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.