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h-STABILITY OF THE NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS VIA t-SIMILARITY

  • Received : 2011.05.11
  • Accepted : 2011.11.18
  • Published : 2011.12.30

Abstract

In this paper, we investigate h-stability of the non-linear perturbed differential systems using the the notion of $t_{\infty}$-similarity.

Keywords

References

  1. V. M. Alekseev, An estimate for the perturbations of the solutions of ordinary differential equations, Vestn. Mosk. Univ. Ser. I. Math. Mekh., 2 (1961), 28- 36(Russian).
  2. S. K. Choi and N. J. Koo, h-stability for nonlinear perturbed systems, Ann. of Diff. Eqs. 11 (1995), 1-9.
  3. S. K. Choi and H. S. Ryu, h-stability in differential systems, Bull. Inst. Math. Acad. Sinica 21 (1993), 245-262.
  4. S. K. Choi and N. J. Koo and H.S. Ryu, h-stability of differential systems via $t_{\infty}$-similarity, Bull. Korean. Math. Soc. 34 (1997), 371-383.
  5. R. Conti, Sulla $t_{\infty}$-similitudine tra matricie l'equivalenza asintotica dei sistemi differenziali lineari, Rivista di Mat. Univ. Parma 8 (1957), 43-47.
  6. S. Elaydi and R. R. M. Rao, Lipschitz stability for nonlinear Volterra integro- differential systems, Appl. Math. Computations 27 (1988), 191-199. https://doi.org/10.1016/0096-3003(88)90001-X
  7. Y . H. Goo , h-stability of the nonlinear differential systems via $t_{\infty}$-similarity, J. Chungcheong Math. Soc. 23 (2010), 383-389.
  8. Y . H. Goo and D. H. Ry , h-stability of the nonlinear perturbed differential systems, J. Chungcheong Math. Soc. 23 (2010), 827-834.
  9. Y . H. Goo and D. H. Ry, h-stability for perturbed integro-differential systems, J. Chungcheong Math. Soc. 21 (2008), 511-517.
  10. Y. H. Goo, M. H. Ji and D. H. Ry, h-stability in certain integro-differential equations, J. Chungcheong Math. Soc. 22 (2009), 81-88.
  11. G. A. Hewer, Stability properties of the equation by $t_{\infty}$-similarity, J. Math. Anal. Appl. 41 (1973), 336-344. https://doi.org/10.1016/0022-247X(73)90209-6
  12. V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications Vol., Academic Press, New York and London, 1969.
  13. M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), 161-175.
  14. M. Pinto, Asymptotic integration of a system resulting from the perturbation of an h-system, J. Math. Anal. Appl. 131 (1988), 194-216. https://doi.org/10.1016/0022-247X(88)90200-4
  15. M. Pinto, Stability of nonlinear differential systems, Applicable Analysis 43 (1992), 1-20. https://doi.org/10.1080/00036819208840049