Exponential dichotomies for almost periodic equations. (English) Zbl 0664.34016
The author considers the equation (1) \(x'=A(t)x\), where A is an \(n\times n\) almost periodic on R matrix function. He shows that if (1) has an exponential dichotomy on a sufficiently long finite interval then it has one on R.
Reviewer: A.Reinfelds (Riga)
MSC:
| 34A30 | Linear ordinary differential equations and systems |
| 34C27 | Almost and pseudo-almost periodic solutions to ordinary differential equations |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
References:
| [1] | W. A. Coppel, Stability and asymptotic behavior of differential equations, D. C. Heath and Co., Boston, Mass., 1965. · Zbl 0154.09301 |
| [2] | W. A. Coppel, Dichotomies in stability theory, Lecture Notes in Mathematics, Vol. 629, Springer-Verlag, Berlin-New York, 1978. · Zbl 0376.34001 |
| [3] | Lawrence Markus and Hidehiko Yamabe, Global stability criteria for differential systems, Osaka Math. J. 12 (1960), 305 – 317. · Zbl 0096.28802 |
| [4] | Kenneth J. Palmer, A perturbation theorem for exponential dichotomies, Proc. Roy. Soc. Edinburgh Sect. A 106 (1987), no. 1-2, 25 – 37. · Zbl 0629.34058 · doi:10.1017/S0308210500018175 |
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