| Title:
|
Banach function spaces and exponential instability of evolution families (English) |
| Author:
|
Megan, Mihail |
| Author:
|
Sasu, Luminita |
| Author:
|
Sasu, Bogdan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
39 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
277-286 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we give necessary and sufficient conditions for uniform exponential instability of evolution families in Banach spaces, in terms of Banach function spaces. Versions of some well-known theorems due to Datko, Neerven, Rolewicz and Zabczyk, are obtained for the case of uniform exponential instability of evolution families. (English) |
| Keyword:
|
evolution family |
| Keyword:
|
uniform exponential instability |
| Keyword:
|
Banach function spaces |
| MSC:
|
34D05 |
| MSC:
|
34D20 |
| MSC:
|
34G10 |
| MSC:
|
34G20 |
| MSC:
|
47D06 |
| idZBL:
|
Zbl 1116.34328 |
| idMR:
|
MR2028738 |
| . |
| Date available:
|
2008-06-06T22:42:17Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107875 |
| . |
| Reference:
|
[1] Chow S. N., Leiva H.: Existence and roughness of the exponential dichotomy for linear skew-product semiflows in Banach space.J. Differential Equations 120 (1995), 429–477. MR 1347351 |
| Reference:
|
[2] Chicone C., Latushkin Y.: Evolution Semigroups in Dynamical Systems and Differential Equations.Math. Surveys Monogr. 70, Amer. Math. Soc., 1999. Zbl 0970.47027, MR 1707332 |
| Reference:
|
[3] Daleckii J. L., Krein M. G.: Stability of Solutions of Differential Equations in Banach Spaces.Transl. Math. Monogr. 43, Amer. Math. Soc., Providence, R.I., 1974. MR 0352639 |
| Reference:
|
[4] Datko R.: Uniform asymptotic stability of evolutionary processes in a Banach space.SIAM J. Math. Anal. 3 (1972), 428–445. Zbl 0241.34071, MR 0320465 |
| Reference:
|
[5] Meyer-Nieberg P.: Banach Lattices.Springer Verlag, Berlin, Heidelberg, New York, 1991. Zbl 0743.46015, MR 1128093 |
| Reference:
|
[6] Megan M., Sasu B., Sasu A. L.: On uniform exponential stability of evolution families.Riv. Mat. Univ. Parma 4 (2001), 27–43. Zbl 1003.34045, MR 1878009 |
| Reference:
|
[7] Megan M., Sasu A. L., Sasu B.: Nonuniform exponential instability of evolution operators in Banach spaces.Glas. Mat. Ser. III 56 (2001), 287–295. MR 1884449 |
| Reference:
|
[8] Megan M., Sasu B., Sasu A. L.: On nonuniform exponential dichotomy of evolution operators in Banach spaces.Integral Equations Operator Theory 44 (2002), 71–78. Zbl 1034.34056, MR 1913424 |
| Reference:
|
[9] Megan M., Sasu A. L., Sasu B.: On uniform exponential stability of linear skew- -product semiflows in Banach spaces.Bull. Belg. Math. Soc. Simon Stevin 9 (2002), 143–154. Zbl 1032.34046, MR 1905653 |
| Reference:
|
[10] Megan M., Sasu A. L., Sasu B.: Discrete admissibility and exponential dichotomy for evolution families.Discrete Contin. Dynam. Systems 9 (2003), 383–397. Zbl 1032.34048, MR 1952381 |
| Reference:
|
[11] Megan M., Sasu A. L., Sasu B.: Theorems of Perron type for uniform exponential dichotomy of linear skew-product semiflows.Bull. Belg. Mat. Soc. Simon Stevin 10 (2003), 1–21. Zbl 1045.34022, MR 2032321 |
| Reference:
|
[12] Megan M., Sasu A. L., Sasu B.: Perron conditions for uniform exponential expansiveness of linear skew-product flows.Monatsh. Math. 138 (2003), 145–157. Zbl 1023.34043, MR 1964462 |
| Reference:
|
[13] Megan M., Sasu B., Sasu A. L.: Exponential expansiveness and complete admissibility for evolution families.Czech. Math. J. 53 (2003). Zbl 1080.34546, MR 2086730 |
| Reference:
|
[14] Megan M., Sasu A. L., Sasu B.: Perron conditions for pointwise and global exponential dichotomy of linear skew-product flows.accepted for publication in Integral Equations Operator Theory. Zbl 1064.34035, MR 2105960 |
| Reference:
|
[15] Megan M., Sasu A. L., Sasu B.: Theorems of Perron type for uniform exponential stability of linear skew-product semiflows.accepted for publication in Dynam. Contin. Discrete Impuls. Systems. Zbl 1079.34047 |
| Reference:
|
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| Reference:
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| Reference:
|
[18] van Neerven J. M. A. M.: The Asymptotic Behaviour of Semigroups of Linear Operators.Operator Theory Adv. Appl. 88, Birkhäuser, Bassel, 1996. Zbl 0905.47001, MR 1409370 |
| Reference:
|
[19] Rolewicz S.: On uniform N - equistability.J. Math. Anal. Appl. 115 (1986), 434–441. Zbl 0597.34064, MR 0836237 |
| Reference:
|
[20] Zabczyk J.: Remarks on the control of discrete-time distributed parameter systems.SIAM J. Control Optim. 12 (1994), 721–735. MR 0410506 |
| . |
