Solvability of a nonlocal boundary-value problem for the operator-differential equation with weak nonlinearity in a refined scale of Sobolev spaces

Abstract

A nonlocal boundary-value problem for the differential equation with weak nonlinearity and with differential operator B = (B 1, …, B p ), where \( {B}_j\equiv {z}_j\frac{\partial }{\partial {z}_j}\;\mathrm{and}\;j=1,\dots, p \) is considered. By using the Nash–Moser iterative scheme, the solvability conditions for the present problem in the Hilbert H¨ormander spaces of functions of many complex variables forming a refined Sobolev scale of spaces is established.