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On nonuniform exponential dichotomy of evolution operators in Banach spaces. (English) Zbl 1034.34056
The authors study the nonuniform exponential dichotomy of evolution operators in Banach spaces. It is shown that $(C_0,C_0)$-admissibility for evolution operators implies nonuniformly exponentially dichotomy, and that the converse generally does not as an example shows. This paper is related to the paper of {\it Nguyen Van Minh, F. Räbiger} and {\it R. Schnaubelt} [Integral Equations Oper. Theory 32, 332--353 (1998; Zbl 0977.34056)], which discussed the uniform case.

34D09Dichotomy, trichotomy
34D05Asymptotic stability of ODE
Full Text: DOI
[1] [BG1] Ben-Artzi A., Gohberg I.,Dichotomies of systems and invertibility of linear ordinary differential operators, Oper. Theory Adv. Appl.,56 (1992), 90-119. · Zbl 0766.47021
[2] [BG2] Ben-Artzi A., Gohberg I.,Dichotomies of perturbed time-varying systems and the power method, Indiana Univ. Math. J.,42 (1993), 699-720. · Zbl 0809.47013 · doi:10.1512/iumj.1993.42.42031
[3] Ben-Artzi A., Gohberg I., Kaashoek M.A.,Invertibility and dichotomy of differential operators on the half-line, J. Dhnam. Differential Equations,5 (1993), 1-36. · Zbl 0771.34011 · doi:10.1007/BF01063733
[4] [DaK] Daleckij J., Krein M.,Stability of Differential Equations in Banach Space, Amer. Math. Soc., Providence, RI, 1974.
[5] [LR] Latushkin Y., Randolph T.,Dichotomy of differential equations on Banach spaces and algebra of weighted translation operators, Integral Equations Operator Theory,23 (1995), 472-500. · Zbl 0839.47026 · doi:10.1007/BF01203919
[6] [LRS] Latushkin Y., Randolph T., Schnaubelt R.Exponential dichotomy and mild solutions of nonautonomous equations in Banach spaces, J. Dynam. Differential Equations,10 (1998), 489-509. · Zbl 0908.34045 · doi:10.1023/A:1022609414870
[7] [MaS] Massera J.J., Sch?ffer, J.L.,Linear Differential Equations and Function Spaces, Academic Press, New-York, 1996.
[8] Megan M.,On (h, k)-dichotomy of evolution operators in Banach spaces, Dynam. Systems Appl.,2 (1996), 189-196. · Zbl 0866.34043
[9] [MSS] Megan M., Sasu A. L., Sasu B.,Discrete admissibility and exponential dichotomy for evolution families, accepted for publication in Discrete Contin. Dynam. Systems · Zbl 1032.34048
[10] [MRS] Van Minh N., R?biger F., Schnaubelt R.,Exponential stability, exponential expansiveness and exponential dichotomy of evolution families on the half-line, Integral Equations Operator Theory,32 (1998), 332-353. · Zbl 0977.34056 · doi:10.1007/BF01203774
[11] [PM] Preda P., Megan M.,Nonuniform dichotomy of evolutionary processes in Banach spaces, Bull. Austral. Math. Soc.,27 (1983), 31-52. · Zbl 0503.34030 · doi:10.1017/S0004972700011473
[12] Sacker R., Sell G.,Dichotomies for linear evolutionary equations in Banach spaces, J. Differential Equations,113, (1994), 17-67. · Zbl 0815.34049 · doi:10.1006/jdeq.1994.1113