×

Discrete dichotomies and asymptotic behavior for abstract retarded functional difference equations in phase space. (English) Zbl 1019.39008

Authors’ abstract: We study the problem of asymptotic behavior between weighted bounded solutions of a system of homogeneous linear functional difference equations and its perturbation under non-classical dichotomic properties and also we obtain some results about approximation. We apply our results to Volterra difference systems with infinite delay.

MSC:

39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
34D09 Dichotomy, trichotomy of solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Coffman C.V., Trans. Am. Math. Soc. 110 pp 22– (1964)
[2] Corduneanu C., Nonlinear Anal. 4 pp 831– (1980) · Zbl 0449.34048
[3] Coppel W.A., Lectures Notes in Mathematics 629, in: Dichotomies in Stability Theory (1978) · Zbl 0376.34001
[4] Cuevas C., J. Difference Eq. Appl. 6 pp 461– (2000) · Zbl 0965.39007
[5] Cuevas C., J. Camp. Appl. Math. 113 pp 217– (2000) · Zbl 0940.39005
[6] Dalietzkii Yu.L., Stability of Solutions of Differential Equations in Banach Spaces (1978)
[7] Drozdowicz A., Proc. Am. Math. Soc. 99 pp 135– (1987)
[8] Elaydi S., J. Difference Eq. Appl. pp 1– (1999) · Zbl 0923.39004
[9] Evgrafov M.A., Dokl. Acad. Nauk., SSSR 121 pp 26– (1958)
[10] Hale J., Funkciolaj Ekoacioj 21 pp 11– (1978)
[11] Henriquez H., Nonlinear Anal. T.MA. 28 (3) pp 513– (1991) · Zbl 0864.35112
[12] Henríquez H., Funkciolaj Ekoacioj 37 (2) pp 329– (1994)
[13] Henríquez H., Indian J. Pure Appl. Math. 27 (4) pp 357– (1996)
[14] Hino Y., Functional Differential Equations with Infinite Delay Lectures Notes in Mathematics 1473 (1991) · Zbl 0732.34051
[15] Levinson N., Am. Math. J. 15 pp 1– (1946) · Zbl 0061.19706
[16] Levinson N., Duke Math. J. 15 pp 129– (1948) · Zbl 0040.19402
[17] Naulin R., J. Differential Eqs. 118 (1) pp 20– (1995) · Zbl 0836.34047
[18] Massera J.L., Linear Differential Equations and Functions Spaces (1966) · Zbl 0243.34107
[19] Morakami, S. Some spectral properties of the solution operator for linear Volterra difference system. Proc. of the third international conference on difference equations. Taipei, China. pp.301–311.
[20] Murakami S., Nonlinear Anal. T.M.A. 30 (2) pp 1153– (1997) · Zbl 0889.39012
[21] Palmer K.J., J. Differential Eqs. 55 pp 225– (1984) · Zbl 0508.58035
[22] Perron O., Math. Zeit. 32 pp 703– (1930) · JFM 56.1040.01
[23] Pinto M., Camp. Math. Anal 28 pp 259– (1994)
[24] Pinto M., Adv. in Diff. Eqs. II Comput. Math Appl. 36 pp 391– (1998)
[25] Poincaré H., Am. J. Math. 7 pp 203– (1885) · JFM 17.0290.01
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.