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Asymptotic formulae for a particular solution of linear nonhomogeneous discrete equations. (English) Zbl 1055.39003
For the difference equation $\Delta u(k)= A(k)u(k)+ g(k)$ the asymptotic behaviour of a particular solution is determined by means of a formal solution. Some examples are discussed.

39A11Stability of difference equations (MSC2000)
Full Text: DOI
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[2] Došlý, O.: Sturm-Liouville dynamic equations on time scales--A unified approach to continuous and discrete oscillation theory. Proceedings of the international scientific conference of mathematics, 49-56 (1998) · Zbl 0933.34025
[3] Györi, I.; Pituk, M.: Asymptotic formulae for the solutions of a linear delay difference equation. J. math. Anal. appl. 195, 376-392 (1995) · Zbl 0846.39003
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[5] Hara, T.; Matsunaga, H.: The asymptotic stability of a two-dimensional linear delay difference equation. Dynamics of cont., discrete and imp. Systems 6, 465-473 (1999) · Zbl 0952.39004
[6] Pituk, M.: Asymptotic behavior of a Poincaré difference equation. J. difference equat. And appl. 3, 33-53 (1997) · Zbl 0874.39008
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[8] Pituk, M.: Convergence and uniform stability in a nonlinear delay difference system. Mathl. comput. Modelling 22, No. 2, 51-58 (1995) · Zbl 0834.39008
[9] Zhang, S.: Stability of infinite delay difference systems. Nonl. anal. T.M.A. 22, 1121-1129 (1994) · Zbl 0822.39002
[10] Zhang, S.: Boundedness of infinite delay difference systems. Nonl. anal. T.M.A. 22, 1209-1219 (1994) · Zbl 0805.39003
[11] Agarwal, R. P.: Differential equations and inequalities, theory, methods, and applications. (1992) · Zbl 0925.39001
[12] Elaydi, S. N.: An introduction to difference equations. (1995) · Zbl 0855.39003
[13] Diblík, J.: Discrete retract principle for systems of discrete equations. Advances in difference equations III special issue of computers math. Applic. 42, No. 3--5, 515-528 (2001) · Zbl 0999.39005