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On uniform exponential \(N\)-dichotomy. (English) Zbl 0844.60032

The authors study the problem of uniform exponential \(N\)-dichotomy of evolutionary processes in Banach spaces. Generalizations of some well-known results of R. Datko, Z. Zabczyk, S. Rolewicz and A. Ichikawa are obtained. The obtained results are applicable for a large class of nonlinear differential equations described by A. Ichikawa.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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References:

[1] Datko, R., Uniform asymptotic stability of evolutionary processes in a Banach space, SIAM J. Math. Anal., 3 (1973), 428-445. · Zbl 0241.34071
[2] Ichikawa, A., Equivalence of Lp stability and exponential stability for a class of nonlinear semigroups, Nonlinear Analysis, Theory, Methods and Applications, vol 8, n° 7 (1984), 805-815. · Zbl 0547.47041
[3] Preda, P., Megan, M., Exponential dichotomy of evolutionary processes in Banach spaces, Czechoslovak Math. Journal, 35 (110) (1985) 312-323. · Zbl 0609.47051
[4] Rolewicz, S., On uniform N-equistability, J. Math. Anal. and Appl. vol 115 (2) (1986), 434-441. · Zbl 0597.34064
[5] Zabczyk, Z., Remarks on the control of discrete-time distributed and parameter systems, SIAM J. Control. Optim.12 (1974), 721-735. · Zbl 0254.93027
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