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

A nonlocal boundary-value problem for the differential equation with weak nonlinearity and with differential operator B = ( B 1 , …, B p ), where B j ≡ z j ∂ ∂ z j and j = 1 , … , 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.