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Asymptotic behavior of nonlinear difference equations with delays. (English) Zbl 1002.39017

The author considers the asymptotic behavior of nonlinear difference equations with delays. Sufficient conditions for an attracting set and a basin of attraction of the equations are obtained. Examples are given to show the applicability of the proposed approach.

MSC:

39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
39A05 General theory of difference equations
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[1] Hale, J.K., Asymptotic behavior of dissipative systems, (1988), Amer. Math. Soc Providence, RI · Zbl 0642.58013
[2] Bates, P.W.; Lu, K.; Zeng, C., Existence and persistence of invariant manifolds for semiflows in Banach space, Memoirs of amer. math. soc., 645, (1998) · Zbl 1023.37013
[3] Temam, R., ()
[4] Ladyzhenskaya, O., Attractor for semigroups and evolution equations, (1991), Cambridge University Press New York
[5] Siljak, D.D., Large-scale dynamic system: stability and structure, (1978), Elsevier North-Holland New York · Zbl 0382.93003
[6] Lasalle, J.P., The stability of dynamical systems, (1976), SIAM Philadelphia, PA · Zbl 0364.93002
[7] Xu, D.Y., Integro-differential equations and delay integral inequalities, Tohoku math. J., 44, 365-378, (1992) · Zbl 0760.34059
[8] Liu, X.Z.; Xu, D.Y., Uniform asymptotic stability of abstract functional differential equations, J. math. anal. appl., 216, 626-643, (1997) · Zbl 0891.34073
[9] Lakshmikantham, V.; Trigiante, D., Theory of difference equations, (1988), Academic Press New York · Zbl 0683.39001
[10] Xu, D.Y., The exponential stability in the large of discrete systems, J. math. research & exposition, 4, 69-72, (1984)
[11] Shi, B.; Wang, Z.C.; Yu, J.S., Asymptotic constancy of solutions of linear parabolic Volterra difference equations, Computers math. applic., 32, 8, 65-77, (1996) · Zbl 0873.39007
[12] Wang, L.; Zhang, Y., Stability of nonlinear analytic difference equations, Atca Mathematica sinica, 38, 355-362, (1995)
[13] Xu, D.Y.; Li, S.Y.; Pu, Z.L.; Guo, Q.Y., Domain of attraction of nonlinear discrete systems with delays, Computers math. applic., 38, 5/6, 155-162, (1999) · Zbl 0939.39013
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