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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 Nguyen Van Minh, F. Räbiger and R. Schnaubelt [Integral Equations Oper. Theory 32, 332–353 (1998; Zbl 0977.34056)], which discussed the uniform case.
MSC:
34D09Dichotomy, trichotomy
34D05Asymptotic stability of ODE
References:
[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.
[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.
[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
[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