Geodesic
Banach function spaces and exponential instability of evolution families
Archivum mathematicum, Tome 39 (2003) no. 4, pp. 277-286
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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.
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.
Classification : 34D05, 34D20, 34G10, 34G20, 47D06
Keywords: evolution family; uniform exponential instability; Banach function spaces 
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Megan, Mihail; Sasu, Luminita; Sasu, Bogdan. Banach function spaces and exponential instability of evolution families. Archivum mathematicum, Tome 39 (2003) no. 4, pp. 277-286. http://geodesic.mathdoc.fr/item/ARM_2003_39_4_a2/

[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

[2] Chicone C., Latushkin Y.: Evolution Semigroups in Dynamical Systems and Differential Equations. Math. Surveys Monogr. 70, Amer. Math. Soc., 1999. | MR | Zbl

[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

[4] Datko R.: Uniform asymptotic stability of evolutionary processes in a Banach space. SIAM J. Math. Anal. 3 (1972), 428–445. | MR | Zbl

[5] Meyer-Nieberg P.: Banach Lattices. Springer Verlag, Berlin, Heidelberg, New York, 1991. | MR | Zbl

[6] Megan M., Sasu B., Sasu A. L.: On uniform exponential stability of evolution families. Riv. Mat. Univ. Parma 4 (2001), 27–43. | MR | Zbl

[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

[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. | MR | Zbl

[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. | MR | Zbl

[10] Megan M., Sasu A. L., Sasu B.: Discrete admissibility and exponential dichotomy for evolution families. Discrete Contin. Dynam. Systems 9 (2003), 383–397. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[13] Megan M., Sasu B., Sasu A. L.: Exponential expansiveness and complete admissibility for evolution families. Czech. Math. J. 53 (2003). | MR | Zbl

[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. | MR | Zbl

[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

[16] van Minh N., Räbiger F., Schnaubelt R.: Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half line. Integral Equations Operator Theory 32 (1998), 332–353. | MR | Zbl

[17] van Neerven J. M. A. M.: Exponential stability of operators and operator semigroups. J. Funct. Anal. 130 (1995), 293–309. | MR | Zbl

[18] van Neerven J. M. A. M.: The Asymptotic Behaviour of Semigroups of Linear Operators. Operator Theory Adv. Appl. 88, Birkhäuser, Bassel, 1996. | MR | Zbl

[19] Rolewicz S.: On uniform N - equistability. J. Math. Anal. Appl. 115 (1986), 434–441. | MR | Zbl

[20] Zabczyk J.: Remarks on the control of discrete-time distributed parameter systems. SIAM J. Control Optim. 12 (1994), 721–735. | MR