Strap N. Problems with non-local conditions for the chosen variable for partial differential equations in the complex domains

The thesis deals with the nonlocal boundary-value problems for the partial differential equations and systems of such equations. А criterion for the unique solvability of these problems and а sufficient conditions for the existence of its solutions are established in Sobolev scale of spaces of functions of several complex variables, in the spaces of functions, which are Dirichlet-Taylor series with fixed spectrum, and in the Hilbert Hormander spaces forming a refined Sobolev scale of spaces. The proof of the solvability of the problem for the partial differential equation with weakly nonlinear right-hand side is carried out within the Nash-Moser iterative scheme. By using the metric approach, the theorems on lower estimates of small denominators appearing in the construction of solutions of the analyzed problems is proved.