Nonlocal Boundary-Value Problem for a Differential-Operator Equation with Weak Nonlinearity in the Spaces of Dirichlet–Taylor Series with Fixed Spectrum

We study the nonlocal boundary-value problem for a differential-operator equation with nonlinear right-hand side and an operator B = (B1,…Bp), where its components Bj ≡ zj∂/∂zj, j = 1,…,p, are the operators of generalized differentiation with respect to the complex variable zj. By using the Nash–Moser iterative scheme, we establish the conditions of solvability of this problem in the scale of spaces of functions of several complex variables, which are Dirichlet–Taylor series with fixed spectrum. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.