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http://dx.doi.org/10.4134/BKMS.2007.44.1.177

ASYMPTOTIC BEHAVIOR OF NONLINEAR VOLTERRA DIFFERENCE SYSTEMS  

Choi, Sung-Kyu (Department of Mathematics Chungnam National University)
Goo, Yoon-Hoe (Department of Mathematics Hanseo University)
Koo, Nam-Jip (Department of Mathematics Chungnam National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.44, no.1, 2007 , pp. 177-184 More about this Journal
Abstract
We study the asymptotic behavior of nonlinear Volterra difference system $$x(n+1)=f(n,x(n))+{\sum\limits^{n}_{s=n_{o}}\;g(n,s,x(s)),\;x(n_{o})=xo$$ by using the resolvent matrix R(n, m) of the corresponding linear Volterra system and the comparison principle.
Keywords
asymptotic equivalence; asymptotic equilibrium; nonlinear Volterra difference system; resolvent matrix; comparison principle;
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1 R. P. Agarwal, Difference Equations and Inequalities, Theory, methods, and applications. Second edition. Monographs and Textbooks in Pure and Applied Mathematics, 228. Marcel Dekker, Inc., New York, 2000
2 F. Brauer, Asymptotic equivalence and asymptotic behaviour of linear systems, Michigan Math. J. 9 (1962), 33-43   DOI
3 S. K. Choi and N. J. Koo, Asymptotic equivalence between two linear Volterra difference systems, Comput. Math. Appl. 47 (2004), no. 2-3, 461-471   DOI   ScienceOn
4 S. K. Choi, N. J. Koo, and Y. H. Goo, Asymptotic property of nonlinear Volterra difference systems, Nonlinear Anal. 51 (2002), no. 2, Ser. A: Theory Methods, 321-337   DOI   ScienceOn
5 S. K. Choi, N. J. Koo, and H. S. Ryu, Asymptotic equivalence between two difference systems, Advances in difference equations, IV., Comput. Math. Appl. 45 (2003), no. 6-9, 1327-1337   DOI   ScienceOn
6 S. Elaydi, Periodicity and stability of linear Volterra difference systems, J. Math. Anal. Appl. 181 (1994), no. 2, 483-492   DOI   ScienceOn
7 V. Lakshmikantham and D. Trigiante, Theory of difference equations, Numerical methods and applications. Mathematics in Science and Engineering, 181. Academic Press, Inc., Boston, MA, 1988
8 M. Zouyousefain and S. Leela, Stability results for difference equations of Volterra type, Appl. Math. Comput. 36 (1990), no. 1, part I, 51-61   DOI   ScienceOn
9 M. Medina, Asymptotic properties of solutions of nonlinear difference equations, J. Comput. Appl. Math. 70 (1996), no. 1, 57-66   DOI   ScienceOn
10 R. Medina and M. Pinto, Asymptotic equivalence and asymptotic behavior of difference systems, Commun. Appl. Anal. 1 (1997), no. 4, 511-523
11 C. Cuevas and M. Pinto, Asymptotic behavior in Volterra difference systems with un-bounded delay, Fixed point theory with applications in nonlinear analysis, J. Comput. Appl. Math. 113 (2000), no. 1-2, 217-225   DOI   ScienceOn
12 W. F. Trench, Linear asymptotic equilibrium and uniform, exponential, and strict stability of linear difference systems, Advances in difference equations, II. Comput. Math. Appl. 36 (1998), no. 10-12, 261-267   DOI   ScienceOn