| Title:
|
Trichotomy and bounded solutions of nonlinear differential equations (English) |
| Author:
|
Cichoń, Mieczysław |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
119 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
275-284 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The existence of bounded solutions for equations $x'=A(t)x+f(t,x)$ in Banach spaces is proved. We assume that the linear part is trichotomic and the perturbation $f$ satisfies some conditions expressed in terms of measures of noncompactness. (English) |
| Keyword:
|
existence |
| Keyword:
|
bounded solutions |
| Keyword:
|
quasilinear differential |
| Keyword:
|
trichotomy |
| Keyword:
|
measures of noncompactness |
| Keyword:
|
Banach spaces |
| MSC:
|
34C11 |
| MSC:
|
34C28 |
| MSC:
|
34G20 |
| MSC:
|
47H15 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0819.34040 |
| idMR:
|
MR1305530 |
| DOI:
|
10.21136/MB.1994.126161 |
| . |
| Date available:
|
2009-09-24T21:06:00Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126161 |
| . |
| Reference:
|
[1] J. Banaś, K. Goebel: Measures of Noncompactness in Banach Spaces.Lect. Notes Pure Applied Math., vol. 60, New York, 1980. MR 0591679 |
| Reference:
|
[2] M. A. Boudourides: On bounded solutions of nonlinear ordinaгy differential equations.Comm. Math. Univ. Carolinae 22 (1981), 15-26. MR 0609933 |
| Reference:
|
[3] M. Cichoń: A point of view on measures of noncompactness.Demonstr. Math. 26 (1993). in press. MR 1265840 |
| Reference:
|
[4] J. L. Daleckii, M. G. Krein: Stability of Solutions of Ordinary Differential Equations in Banach Spaces.Moscow, 1970. (In Russian.) |
| Reference:
|
[5] M. Dawidowski, B. Rzepecki: On bounded solutions of nonlinear differential equations in Banach spaces.Demonstratio Math. 18 (1985), 91-102. Zbl 0593.34062, MR 0816022 |
| Reference:
|
[6] S. Elaydi, O. Hajek: Exponential trichotomy of differential systems.Јouг. Math. Anal. Appl. 129 (1988), 362-374. Zbl 0651.34052, MR 0924294, 10.1016/0022-247X(88)90255-7 |
| Reference:
|
[7] S. Elaydi, O. Hajek: Exponential dichotomy and trichotomy of nonlinear differential equations.Diff. Integral Equations 3 (1990), 1201-1204. Zbl 0722.34053, MR 1073067 |
| Reference:
|
[8] D. L. Lovelady: Bounded solutions of whole-line differential equations.Bull. AMS 79 (1972), 752-753. MR 0322267 |
| Reference:
|
[9] J. L. Massera, J. J. Schäffer: Linear Differential Equations and Function Spaces.New York-London, 1966. MR 0212324 |
| Reference:
|
[10] P. Preda, M. Megan: Exponential dichotomy of evolutionary processes in Banach spaces.Czechoslovak Math. Јour. 35 (1985), 312-323. Zbl 0609.47051, MR 0787133 |
| Reference:
|
[11] B. Przeradzki: The existence of bounded solutions for differential equations in Hilbert spaces.Ann. Polon. Math. 56 (1992), 103-121. Zbl 0805.47041, MR 1159982, 10.4064/ap-56-2-103-121 |
| Reference:
|
[12] B. N. Sadovskii: A fixed point principle.Functional Analysis and its Applications 1 (1967), 151-153. (In Russian.) MR 0211302 |
| Reference:
|
[13] S. Szufla: On the existence of bounded solutions of nonlinear differential equations in Banach spaces.Funct. Approx. 15 (1986), 117-123. Zbl 0617.34061, MR 0880140 |
| . |
