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http://dx.doi.org/10.4134/CKMS.2011.26.1.037

ASYMPTOTIC EQUIVALENCE FOR LINEAR DIFFERENTIAL SYSTEMS  

Choi, Sung-Kyu (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY)
Koo, Nam-Jip (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY)
Lee, Keon-Hee (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.26, no.1, 2011 , pp. 37-49 More about this Journal
Abstract
We investigate the asymptotic equivalence for linear differential systems by means of the notions of $t_{\infty}$-similarity and strong stability.
Keywords
linear differential system; adjoint system; strong stability; $t_{\infty}$-similarity; linear asymptotic equilibrium; asymptotic equivalence;
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Times Cited By KSCI : 2  (Citation Analysis)
Times Cited By SCOPUS : 0
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1 G. Sansone and R. Conti, Non-linear Differential Equatioins, The Macmillan Company, New York, 1964.
2 W. F. Trench, On $t_{\infty}$ quasisimilarity of linear systems, Ann. Mat. Pura Appl. (4) 142 (1985), 293-302.   DOI
3 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.
4 S. K. Choi and N. J. Koo, Variationally stable difference systems by $n_{\infty}-similarity$, J. Math. Anal. Appl. 249 (2000), no. 2, 553-568.   DOI   ScienceOn
5 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
6 S. K. Choi, N. J. Koo, and S. Dontha, Asymptotic property in variation for nonlinear differential systems, Appl. Math. Lett. 18 (2005), no. 1, 117-126.   DOI   ScienceOn
7 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
8 S. K. Choi, N. J. Koo, and D. M. Im, Asymptotic equivalence between linear differential systems, Bull. Korean Math. Soc. 42 (2005), no. 4, 691-701.   과학기술학회마을   DOI   ScienceOn
9 S. K. Choi, N. J. Koo, and H. S. Ryu, h-stability of differential systems via $t_{\infty}-similarity$, Bull. Korean Math. Soc. 34 (1997), no. 3, 371-383.   과학기술학회마을
10 R. Conti, Sulla t-similitudine tra matrici e la stabilita dei sistemi differenziali lineari, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8) 19 (1955), 247-250.
11 L. A. Lusternik and W. S. Sobolev, Functional Analysis, Science, Moscov, 1965.
12 R. Conti, Linear differential equations asymptotically equivalent to x = 0, Riv. Mat. Univ. Parma (4) 5 (1979), part 2, 847-853.
13 W. A. Coppel, Stability and Asymptotic Behavior of Differential Equations, D. C. Heath and Company, Boston, 1965.
14 G. A. Hewer, Stability properties of the equation of first variation by $t_{\infty}-similarity$, J. Math. Anal. Appl. 41 (1973), 336-344.   DOI
15 L. Cesari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Academic Press Inc., Publishers, New York; Springer-Verlag, Berlin-Gottingen-Heidelberg, 1963.
16 G. Ascoli, Osservazioni sopra alcune questioni di stabilita. I, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8) 9 (1950), 129-134.