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

Resumo

We study the nonlocal boundary-value problem for a differential-operator equation with nonlinear right-hand side and an operator B = (B₁,…B_p), where its components B_j ≡ z_j∂/∂z_j, j = 1,…,p, are the operators of generalized differentiation with respect to the complex variable z_j. 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.