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

被引：0

作者：

Il'kiv, V. S. ^{[1
]}

Strap, N. I. ^{[1
]}

Volyanska, I. I. ^{[1
]}

机构：

[1] Lvivs Ka Politekhn Natl Univ, Lvov, Ukraine

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2020年 / 72卷 / 04期

关键词：

PERIODIC-SOLUTIONS; CANTOR FAMILIES;

D O I：

10.1007/s11253-020-01798-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Hormander spaces of functions of several real variables, which form a refined Sobolev scale.

引用

页码：515 / 535

页数：21

共 34 条

[1] 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
V. S. Il’kiv
N. I. Strap
I. I. Volyanska
Ukrainian Mathematical Journal, 2020, 72 : 515 - 535
[2] Solvability of a nonlocal boundary-value problem for the operator-differential equation with weak nonlinearity in a refined scale of sobolev spaces
Il’kiv V.S.
Strap N.I.
Journal of Mathematical Sciences, 2016, 218 (1) : 1 - 15
[3] Conditions of solvability of the nonlocal boundary-value problem for a differential-operator equation with weak nonlinearity
Il’kiv V.S.
Strap N.I.
Volyanska I.I.
Journal of Mathematical Sciences, 2021, 256 (6) : 753 - 769
[4] Solvability of the Nonlocal Boundary-Value Problem for a System of Differential-Operator Equations in the Sobolev Scale of Spaces and in a Refined Scale
V. S. Il’kiv
N. I. Strap
Ukrainian Mathematical Journal, 2015, 67 : 690 - 710
[5] Solvability of the Nonlocal Boundary-Value Problem for a System of Differential-Operator Equations in the Sobolev Scale of Spaces and in a Refined Scale
Ilkiv, V. S.
Strap, N. I.
UKRAINIAN MATHEMATICAL JOURNAL, 2015, 67 (05) : 690 - 710
[6] Nonlocal Boundary-Value Problem for a Differential-Operator Equation with Weak Nonlinearity in the Spaces of Dirichlet–Taylor Series with Fixed Spectrum
Il’kiv V.S.
Strap N.I.
Journal of Mathematical Sciences, 2018, 231 (4) : 572 - 585
[7] Nonlocal Boundary-Value Problem for an Equation with Differentiation Operator z ∂/∂z in a Refined Sobolev Scale
Ilkiv V.S.
Strap N.І.
Volyanska І.І.
Journal of Mathematical Sciences, 2023, 273 (6) : 885 - 900
[8] Solvability of the boundary-value problem for the second-order elliptic differential-operator equation with spectral parameter in the equation and boundary conditions
B. A. Aliev
Ukrainian Mathematical Journal, 2010, 62 : 1 - 14
[9] SOLVABILITY OF THE BOUNDARY-VALUE PROBLEM FOR THE SECOND-ORDER ELLIPTIC DIFFERENTIAL-OPERATOR EQUATION WITH SPECTRAL PARAMETER IN THE EQUATION AND BOUNDARY CONDITIONS
Aliev, B. A.
UKRAINIAN MATHEMATICAL JOURNAL, 2010, 62 (01) : 1 - 14
[10] SOLVABILITY OF BOUNDARY VALUE PROBLEM FOR SECOND ORDER ELLIPTIC DIFFERENTIAL-OPERATOR EQUATION WITH SPECTRAL PARAMETER IN THE EQUATION AND BOUNDARY CONDITIONS
Aliev, Bahram A.
PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2010, 33 (41): : 3 - 26

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