| Title:
|
Correct solvability of a general differential equation of the first order in the space $L_p(\mathbb{R})$ (English) |
| Author:
|
Chernyavskaya, N. |
| Author:
|
Shuster, L. A. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
87-105 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the equation \begin{equation} - r(x)y^{\prime }(x)+q(x)y(x)=f(x)\,,\quad x\in \mathbb{R} \end{equation} where $f\in L_p(\mathbb{R}) $, $p\in [1,\infty ]$ ($L_\infty (\mathbb{R}):=C(\mathbb{R})$) and \begin{equation} 0<r\in C^{}(\mathbb{R})\,,\quad 0\le q\in L_1^{}(\mathbb{R})\,. \end{equation} We obtain minimal requirements to the functions $r$ and $q$, in addition to (), under which equation () is correctly solvable in $L_p(\mathbb{R})$, $p\in [1,\infty ]$. (English) |
| Keyword:
|
correct solvability |
| Keyword:
|
differential equation of the first order |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 06487023 |
| idMR:
|
MR3367095 |
| DOI:
|
10.5817/AM2015-2-87 |
| . |
| Date available:
|
2015-06-24T13:39:56Z |
| Last updated:
|
2023-10-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144309 |
| . |
| Reference:
|
[1] Chernyavskaya, N.: Conditions for correct solvability of a simplest singular boundary value problem.Math. Nachr. 243 (2002), 5–18. Zbl 1028.34018, MR 1923831, 10.1002/1522-2616(200209)243:1<5::AID-MANA5>3.0.CO;2-B |
| Reference:
|
[2] Chernyavskaya, N., Shuster, L.: Conditions for correct solvability of a simplest singular boundary value problem of general form. I.Z. Anal. Anwendungen 25 (2006), 205–235. Zbl 1122.34021, MR 2229446, 10.4171/ZAA/1285 |
| Reference:
|
[3] Chernyavskaya, N., Shuster, L.: Conditions for correct solvability of a simplest singular boundary value problem of general form. II.Z. Anal. Anwendungen 26 (2007), 439–458. Zbl 1139.34010, MR 2341766, 10.4171/ZAA/1334 |
| Reference:
|
[4] Kantorovich, L.W., Akilov, G.P.: Functional Analysis.Nauka, Moscow, 1977. MR 0511615 |
| Reference:
|
[5] Lukachev, M., Shuster, L.: On uniqueness of soltuion of a linear differential equation without boundary conditions.Funct. Differ. Equ. 14 (2007), 337–346. MR 2323215 |
| Reference:
|
[6] Mynbaev, K., Otelbaev, M.: Weighted Function Spaces and the Spectrum of Differential Operators.Nauka, Moscow, 1988. MR 0950172 |
| Reference:
|
[7] Opic, B., Kufner, A.: Hardy Type Inequalities.Pitman Research Notes in Mathematics Series, vol. 219, Harlow, Longman, 1990. Zbl 0698.26007, MR 1069756 |
| Reference:
|
[8] Otelbaev, M.: Estimates of the Spectrum of the Sturm-Liouville Operator.Alma-Ata, Gilim, 1990, in Russian. Zbl 0747.47029 |
| . |
