Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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h-STABILITY OF THE NONLINEAR PERTURBED DIFFERENCE SYSTEMS VIA n∞-SIMILARITY

  • 투고 : 2012.06.23
  • 심사 : 2012.11.20
  • 발행 : 2013.01.30
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초록

In this paper, we investigate $h$-stability of the nonlinear perturbed difference system via $n_{\infty}$-similarity.

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참고문헌

  1. R. P. Agarwal, Difference equations and inequalities, Marcel Decker Inc., New York, 1992.
  2. S. K. Choi and N. J. Koo, Stability in variation for nonlinear Volterra difference systems, Bull. Korean Math. Soc. 38 (2001), 101-111.
  3. 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
  4. S. K. Choi and N. J. Koo, Asymptotic Equivalence between two linear Volterra difference systems, Comput.Math. Appl. 47(2004),461-471 https://doi.org/10.1016/S0898-1221(04)90038-7
  5. S. K. Choi, N. J. Koo, and Y. H. Goo, Variationally stable difference systems, J. Math.Anal. Appl. 256 (2001), 587-605. https://doi.org/10.1006/jmaa.2000.7330
  6. S. K. Choi, N. J. Koo, and Y. H. Goo, h-stability of perturbed Volterra difference systems, Bull. Korean Math. Soc. 39 (2002), 53-62. https://doi.org/10.4134/BKMS.2002.39.1.053
  7. S. K. Choi, N. J. Koo, and Y. H. Goo, Asymptotic property of nonlinear Volterra difference systems, Nonlinear Analysis 51 (2002), 321-337. https://doi.org/10.1016/S0362-546X(01)00833-1
  8. S. K. Choi , Y. H. Goo and N. J. Koo, Asymptotic behavior of nonlinear Volterra difference systems, Bull. Korean Math. Soc. 44 (2007), 177-184. https://doi.org/10.4134/BKMS.2007.44.1.177
  9. Y. H. Goo and H. J. Park, h-stability of the nonlinear perturbed difference systems, J.Chungcheong Math. Soc. 24 (2011), 105-112.
  10. Y. H. Goo, h-stability of perturbed differential systems via $t_{\infty}$-similarity, J. Appl.Math. Informatics, 30(3-4) (2012), 511-516.
  11. S. Elaydi and S. Murakami, Uniform asymptotic stability in linear Volterra difference equation, J. Diff. Eqns. Appl. 31 (1998), 203-218.
  12. V. Lakshmikantham and D. Trigiante, Theory of Difference Equations:with Applications to Numerical Methods and Applications, Second Edition, Marcel Dekker, Inc.,2002.
  13. R. Medina, Stability results for nonlinear difference equations, Nonlinear Studies, 6 (1999), 73-83.
  14. R. Medina and M. Pinto, Stability of nonlinear difference equations, Proc. Dynamic Systems and Appl. 2 (1996), 397-404.
  15. R. Medina and M. Pinto, Variationlly stable difference equations, Nonlinear Analysis TMA 30 (1997), 1141-1152. https://doi.org/10.1016/S0362-546X(96)00111-3
  16. Y. N. Raffoul, Boundedness and Periodicity of Volterra system of difference equations, J. Diff. Eqns. Appl. 4 (1998), 381-393. https://doi.org/10.1080/10236199808808150
  17. M. Zouyousefain and S. Leela, Stability results for difference equations of Volterra type, Appl. Math. Compu. 36 (1990), 51-61. https://doi.org/10.1016/0096-3003(90)90074-D