Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ASYMPTOTIC EQUIVALENCE BETWEEN LINEAR DIFFERENTIAL SYSTEMS

  • Choi, Sung-Kyu (DEPARTMENT OF MATHEMATICS, CHUNGNAM NATIONAL UNIVERSITY) ;
  • Koo, Nam-Jip (DEPARTMENT OF MATHEMATICS EDUCATION, CHONGJU UNIVERSITY) ;
  • Im, Dong-Man (DEPARTMANT OF MATHEMATICS EDUCATION, CHONGJU UNIVERSITY)
  • Published : 2005.11.01
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Abstract

We study the strong stability for linear differential systems in connection with too-similarity, and investigate the asymptotic equivalence between linear differential systems.

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References

  1. L. Cesari, Asymptotic Behavior and Stability Properties in Ordinary Differential Equations, Academic Press, Springer-Verlag, 1963
  2. S. K. Choi and N. J. Koo, Variationally stable difference systems by $n_\infty$- similarity, J. Math. Anal. Appl. 249 (2000), 553-568 https://doi.org/10.1006/jmaa.2000.6910
  3. S. K. Choi, N. J. Koo, and H. S. Ryu, Asymptotic equivalence between two difference systems, Computers Math. Appl. 45 (2003), 1327-1337 https://doi.org/10.1016/S0898-1221(03)00106-8
  4. R. Conti, Sulla $t_\infty$-similitudine tra matrici e l'equivalenza asintotica dei sistemi differenziali lineari, Rivista di Mat. Univ. Parma 8 (1957), 43-47
  5. W. A. Coppel, Stability and Asymptotic Behavior of Differential Equations, D. C. Heath and Company, Boston, 1965
  6. G. A. Hewer, Stability properites of the equations of first variation by $t_\infty$- similarity, J. Math. Anal. Appl. 41 (1973), 336-344 https://doi.org/10.1016/0022-247X(73)90209-6
  7. V. Lakshmikantham and S. Leela, Differential and Integral Inequalites with Theory and Applications, Academic Press, New York and London, 1969
  8. M. Pinto, Asymptotic integration of a system resulting from the perturbation of an h-system, J. Math. Anal. Appl. 131 (1985), 194-216 https://doi.org/10.1063/1.35325
  9. W. F. Trench, On $t_\infty$-quasisimilarity of linear systems, Ann. Mat. Pura Appl. 142 (1985), 297-302

Cited by

  1. ASYMPTOTIC EQUIVALENCE FOR LINEAR DIFFERENTIAL SYSTEMS vol.26, pp.1, 2011, https://doi.org/10.4134/CKMS.2011.26.1.037
  2. ASYMPTOTIC EQUIVALENCE BETWEEN TWO LINEAR DYNAMIC SYSTEMS ON TIME SCALES vol.51, pp.4, 2014, https://doi.org/10.4134/BKMS.2014.51.4.1075