| Title:
|
The fixed point theorem and the boundedness of solutions of differential equations in the Banach space (English) |
| Author:
|
Tumajer, František |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
118 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
1-9 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The properties of solutions of the nonlinear differential equation $x'=A(s)x+f(s,x)$ in a Banach space and of the special case of the homogeneous linear differential equation $x'=A(s)x$ are studied. Theorems and conditions guaranteeing boundedness of the solution of the nonlinear equation are given on the assumption that the solutions of the linear homogeneous equation have certain properties. (English) |
| Keyword:
|
differential equation |
| Keyword:
|
Banach space |
| Keyword:
|
existence |
| Keyword:
|
uniqueness |
| Keyword:
|
boundedness |
| Keyword:
|
bounded solution |
| Keyword:
|
derivative of the norm of a linear mapping |
| Keyword:
|
fixed point |
| MSC:
|
34C11 |
| MSC:
|
34G20 |
| MSC:
|
47H10 |
| MSC:
|
47H15 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0776.34052 |
| idMR:
|
MR1213827 |
| DOI:
|
10.21136/MB.1993.126016 |
| . |
| Date available:
|
2009-09-24T20:56:22Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126016 |
| . |
| Reference:
|
[1] J. L. Massera J. J. Schäffler: Linear differential equations and function spaces.Academic press, New York and London, 1966. MR 0212324 |
| Reference:
|
[2] F. Tumajer: The derivative of the norm of the linear mapping and its application to differential equations.Aplikace matematiky 57 (1992), 193-200. MR 1157455 |
| Reference:
|
[3] M. Greguš M. Švec V. Šeda: Ordinary differential equations.Praha, 1985. (In Slovak.) |
| Reference:
|
[4] S. G. Krein M. I. Khazan: Differential equations in a Banach space.Mathem. analysis Vol. 21, Itogi Nauki i Tekhniky, Akad. Nauk SSSR, Vsesojuz. Inst. Nauki i Tekh, Informatsii, Moscow, 1983, pp. 130-264. MR 0736523 |
| Reference:
|
[5] V. V. Vasil'ev S. G. Krejn S. I. Piskarev: Pologruppy operatorov, kosinus operator-funkcii i linejnye differencial'nye uravnenija.Itogi Nauki i Tekhniki, Matematiceskij analiz T. 28, Moskva, 1990, pp. 87-203. |
| Reference:
|
[6] B. Rzepecki: An existence theorem for ordinary differential equations in Banach spaces.Bull. Austral. Soc. 30 no. 3 (1984), 449-456. Zbl 0561.34042, MR 0766802, 10.1017/S0004972700002161 |
| Reference:
|
[7] B. Rzepecki: An existence theorem for bounded solutions of differential equations in Banach spaces.Rend. Sem. Mat. Univ. Padova 13 (1985), 89-94. Zbl 0586.34052, MR 0799899 |
| . |
