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.
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Translated from Ukrains’ki˘ı Matematychny˘ı Visnyk, Vol. 12, No. 4, pp. 437–455, September–December, 2015.
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Il’kiv, V.S., Strap, N.I. Solvability of a nonlocal boundary-value problem for the operator-differential equation with weak nonlinearity in a refined scale of Sobolev spaces. J Math Sci 218, 1–15 (2016). https://doi.org/10.1007/s10958-016-3006-8
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DOI: https://doi.org/10.1007/s10958-016-3006-8