### Non-local boundary value problem for a system of partial differential equations with operator coefficients in a complex domain

#### Abstract

The paper is devoted to investigation of non-local boundary problem for a system of partial differential equations with the operator $B=(B_1,\ldots,B_p)$, where $B_j\equiv z_j\frac{\partial}{\partial z_j}$, $j=1,\ldots,p$, are operators of the generalized differentiation, which operates on complex variable $z_j$. Problem is incorrect in the Hadamard sense and the solvability of this problem depends on the small denominators which arising in the construction of the solution. By using of metric approach, the theorem about lower estimation of small denominators was proved, and also existence and uniqueness conditions of this solution in the scale of spaces of many complex variables functions are establish.

#### Keywords

partial differential equation, operator of generalized differentiation, pseudo-differential operator, small denominators, metric estimation

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