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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Vydáno v:Ukrainian mathematical journal Ročník 72; číslo 4; s. 515 - 535
Hlavní autoři: Il’kiv, V. S., Strap, N. I., Volyanska, I. I.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.09.2020
Springer
Springer Nature B.V
Témata:
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
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-020-01798-7