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29 June 2004 Accurate solution estimates for nonlinear nonautonomous vector difference equations
Rigoberto Medina, M. I. Gil'
Abstr. Appl. Anal. 2004(7): 603-611 (29 June 2004). DOI: 10.1155/S1085337504306184


The paper deals with the vector discrete dynamical system xk+1=Akxk+fk(xk). The well-known result by Perron states that this system is asymptotically stable if AkA=const is stable and fk(x)f˜(x)=o(x). Perron's result gives no information about the size of the region of asymptotic stability and norms of solutions. In this paper, accurate estimates for the norms of solutions are derived. They give us stability conditions for (1.1) and bounds for the region of attraction of the stationary solution. Our approach is based on the “freezing” method for difference equations and on recent estimates for the powers of a constant matrix. We also discuss applications of our main result to partial reaction-diffusion difference equations.


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Rigoberto Medina. M. I. Gil'. "Accurate solution estimates for nonlinear nonautonomous vector difference equations." Abstr. Appl. Anal. 2004 (7) 603 - 611, 29 June 2004.


Published: 29 June 2004
First available in Project Euclid: 7 July 2004

zbMATH: 1099.39011
MathSciNet: MR2084939
Digital Object Identifier: 10.1155/S1085337504306184

Primary: 39A10

Rights: Copyright © 2004 Hindawi

Vol.2004 • No. 7 • 29 June 2004
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