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Variationally stable difference systems. (English) Zbl 0976.39002
The authors derive $h$-stability conditions (defined in the paper) for nonlinear difference systems $$x(n+1)=f(n,x(n))$$ and their perturbed difference systems $$y(n+1)=f(n,y(n))+g(n,y(n)),$$ where $x(n)$ and $y(n)$ are appropriately defined in the paper.

MSC:
39A11Stability of difference equations (MSC2000)
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References:
[1] Agarwal, R. P.: Difference equations and inequalities--theory, methods, and applications. (2000) · Zbl 0952.39001
[2] Athanassov, Z. S.: Perturbation theorems for nonlinear systems of ordinary differential equations. J. math. Anal. appl. 86, 194-207 (1982) · Zbl 0508.34036
[3] Choi, S. K.; Goo, Y. H.; Koo, N. J.: Lipschitz stability and exponential asymptotic stability for the nonlinear functional differential systems. Dynam. systems appl. 6, 397-410 (1997) · Zbl 0890.34061
[4] Choi, S. K.; Koo, N. J.: Variationally stable difference systems by n\infty-similarity. J. math. Anal. appl. 249, 553-568 (2000) · Zbl 0965.39001
[5] Choi, S. K.; Koo, N. J.; Ryu, H. S.: H-stability of differential systems via t\infty-similarity. Bull. korean math. Soc. 34, 371-383 (1997) · Zbl 0891.34059
[6] Hewer, G. A.: Stability properties of the equations of first variation by t\infty-similarity. J. math. Anal. appl. 41, 336-344 (1973) · Zbl 0256.34063
[7] Lakshmikantham, V.; Trigiante, D.: Theory of difference equations with applications to numerical analysis. (1988) · Zbl 0683.39001
[8] Medina, R.: Stability for nonlinear difference systems. Dynam. systems appl. 9, 1-14 (2000)
[9] Medina, R.: Perturbations of nonlinear systems of difference equations. J. math. Anal. appl. 204, 545-553 (1996) · Zbl 0873.39005
[10] Medina, R.: Stability and asymptotic behavior of difference equations. J. comput. Appl. math. 80, 17-30 (1997) · Zbl 0877.39006
[11] Medina, R.: Asymptotic behavior of nonlinear difference systems. J. math. Anal. appl. 219, 294-311 (1998) · Zbl 0908.39002
[12] Medina, R.: Stability results for nonlinear difference equations. Nonlinear stud. 6, 73-83 (1999) · Zbl 0960.39007
[13] Medina, R.; Pinto, M.: Stability of nonlinear difference equations. Proc. dynam. Systems appl. 2, 397-404 (1996) · Zbl 0861.39004
[14] Medina, R.; Pinto, M.: Variationally stable difference equations. Nonlinear anal. 30, 1141-1152 (1997) · Zbl 0889.39004
[15] Sheng, Q.; Agarwal, P.: On nonlinear variation of parameter methods for summary difference equations. Dynam. systems appl. 2, 227-242 (1993) · Zbl 0794.39004