Solvability Conditions for the Nonlocal Boundary-Value Problem for a Differential-Operator Equation with Weak Nonlinearity in the Refined Sobolev Scale of Spaces of Functions of Many Real Variables

We study the solvability of the nonlocal boundary-value problem for a differential equation with weak nonlinearity. By using the Nash–Mozer iterative scheme, we establish the solvability conditions for the posed problem in the Hilbert H¨ormander spaces of functions of several real variables, which f...

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Bibliographic Details
Published in:Ukrainian mathematical journal Vol. 72; no. 4; pp. 515 - 535
Main Authors: Il’kiv, V. S., Strap, N. I., Volyanska, I. I.
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2020
Springer
Springer Nature B.V
Subjects:
Algebra
Analysis
Applications of Mathematics
Boundary value problems
Differential equations
Geometry
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Operators (mathematics)
Real variables
Statistics
ISSN:0041-5995, 1573-9376
Online Access:Get full text
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Summary:We study the solvability of the nonlocal boundary-value problem for a differential equation with weak nonlinearity. By using the Nash–Mozer iterative scheme, we establish the solvability conditions for the posed problem in the Hilbert H¨ormander spaces of functions of several real variables, which form a refined Sobolev scale.
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ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-020-01798-7