A nonlocal boundary-value problem for a fourth-order mixed-type equation

被引：0

作者：

Fayazov K.S. ^{[1
]}

Khajiev I.O. ^{[1
,2
]}

机构：

[1] Turin Polytechnic University in Tashkent, Tashkent

[2] National University of Uzbekistan, Turin Polytechnic University in Tashkent, Tashkent

来源：

Journal of Mathematical Sciences | 2020年 / 248卷 / 2期

关键词：

fourth-order partial differential equations; ill-posed problem; Mixed type equations; nonlocal problem; small denominators; stability; uniqueness;

D O I：

10.1007/s10958-020-04866-2

中图分类号：

学科分类号：

摘要：

The criterion of uniqueness of a solution of the problem with periodicity and nonlocal and boundary conditions is established by the spectral analysis for a fourth-order mixed-type equation in a rectangular region. When constructing a solution in the form of the sum of a series, we use the completeness in the space L2; the system of eigenfunctions of the corresponding problem orthogonally conjugate. When proving the convergence of a series, the problem of small denominators arises. Under some conditions imposed on the parameters of the data of the problem and given functions, the stability of the solution is proved. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

引用

页码：166 / 174

页数：8

共 50 条

[1] On a nonlocal problem for a fourth-order mixed-type equation with the Hilfer operator
Kadirkulov, B. J.
Jalilov, M. A.
[J]. BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2021, 104 (04): : 89 - 102
[2] REGULAR SOLUTION TO A NONLOCAL BOUNDARY-VALUE PROBLEM FOR AN EQUATION OF MIXED-TYPE
KARATOPRAKLIEVA, MG
[J]. DIFFERENTIAL EQUATIONS, 1994, 30 (05) : 780 - 790
[3] A boundary value problem for the fourth-order degenerate equation of the mixed type
Otarova, J. A.
[J]. BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2024, 113 (01): : 140 - 148
[4] Periodic Boundary-Value Problem for a Fourth-Order Differential Equation
Abdullaev, A. R.
Skachkova, E. A.
[J]. RUSSIAN MATHEMATICS, 2013, 57 (12) : 1 - 7
[5] A NONLOCAL BOUNDARY-VALUE PROBLEM FOR AN EQUATION OF MIXED TYPE
KARATOPRAKLIEVA, MG
[J]. DIFFERENTIAL EQUATIONS, 1991, 27 (01) : 54 - 63
[6] On a nonlocal boundary value problem for a fourth-order ordinary differential equation
Jangveladze, T. A.
Lobjanidze, G. B.
[J]. DIFFERENTIAL EQUATIONS, 2011, 47 (02) : 179 - 186
[7] On a nonlocal boundary value problem for a fourth-order ordinary differential equation
T. A. Jangveladze
G. B. Lobjanidze
[J]. Differential Equations, 2011, 47 : 179 - 186
[8] Urinov, On one problem for a fourth-order mixed-type equation that degenerates inside and on the boundary of a domain
Urinov, A. K.
Usmonov, D. A.
[J]. VESTNIK UDMURTSKOGO UNIVERSITETA-MATEMATIKA MEKHANIKA KOMPYUTERNYE NAUKI, 2023, 33 (02): : 312 - 328
[9] INTEGRAL-EQUATION SYSTEM FOR NEWMANN BOUNDARY-VALUE PROBLEM FOR FOURTH-ORDER EQUATION
WICKEL, W
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1978, 58 (07): : T401 - T403
[10] On a Frankl-Type Boundary-Value Problem for a Mixed-Type Degenerating Equation
Islomov, B. I.
Ochilova, N. K.
Sadarangani, K. S.
[J]. UKRAINIAN MATHEMATICAL JOURNAL, 2020, 71 (10) : 1541 - 1554

← 1 2 3 4 5 →