On exponential trichotomy of linear difference equations. (English) Zbl 0687.39003

We start by giving a necessary and sufficient condition in order a linear difference equation to have an exponential trichotomy. The roughness of exponential trichotomy is also proved. A corollary following from the roughness shows that an upper triangular system has an exponential trichotomy if its corresponding diagonal equation has one. Finally we find a relationship between the bounded solutions of a linear equation which has an exponential trichotomy and the bounded solutions of a perturbed equation derived from the linear equation by edding some certain perturbations.
Reviewer: G.Papaschinopoulos


39A10 Additive difference equations
39A11 Stability of difference equations (MSC2000)
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[1] Papaschinopoulos G., Rend. Sem . Fac . Sci . Univ . Cagiari 54 pp 61– (1984)
[2] Papaschinopoulos G., Czechoslovak Math. J_ 35 pp 295– (1985)
[3] Papaschinopoulos G., Bol 1 , Un. Math. Ital 6 pp 61– (1985)
[4] DOI: 10.1016/0022-247X(87)90127-2 · Zbl 0628.39001
[5] DOI: 10.1155/S0161171288000961 · Zbl 0662.39002
[6] Papaschinopoulos G., Ann . Soc . Sci.Bruxelles 102 pp 19– (1988)
[7] Kurzweil J., Czechoslovak Math. J_ 38 pp 280– (1988)
[8] Papaschinopoulos G., J_. Math.Anal. Appl 38 (1988)
[9] DOI: 10.1016/0022-247X(88)90255-7 · Zbl 0651.34052
[10] DOI: 10.1007/BFb0065310
[11] Henry D., Geometric theory of semilinear parabolic equations (1981) · Zbl 0456.35001
[12] Hale J.K., Ordinary differential equations (1969) · Zbl 0186.40901
[13] DOI: 10.1112/blms/5.3.275 · Zbl 0267.58010
[14] Papaschinopoulos G., Math. Japon 33 pp 457– (1988)
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