DOI QR코드

DOI QR Code

BOUNDEDNESS IN PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS VIA t-SIMILARITY

  • Received : 2015.01.14
  • Accepted : 2015.06.02
  • Published : 2015.06.30

Abstract

In this paper, we investigate bounds for solutions of perturbed functional differential systems using 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, 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. Y. H. Goo, Boundedness in perturbed nonlinear differential systems, J. Chungcheong Math. Soc. 26 (2013), 605-613. https://doi.org/10.14403/jcms.2013.26.3.605
  7. Y. H. Goo, Boundedness in the perturbed differential systems, J. Korean Soc. Math. Edu. Ser.B: Pure Appl. Math. 20 (2013), 223-232.
  8. Y. H. Goo, Boundedness in the perturbed nonlinear differential systems, Far East J. Math. Sci(FJMS) Vol.79 (2013), 205-217.
  9. Y. H. Goo, D. G. Park and D. H Ryu, Boundedness in perturbed differential systems, J. Appl. Math. and Informatics 30 (2012), 279-287.
  10. 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
  11. V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications, Academic Press, New York and London, 1969.
  12. B.G. Pachpatte, On some retarded inequalities and applications, J. Ineq. Pure Appl. Math. 3 (2002), 1-7.
  13. M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), 161-175.
  14. M. Pinto, Stability of nonlinear differential systems, Applicable Analysis 43 (1992), 1-20. https://doi.org/10.1080/00036819208840049

Cited by

  1. BOUNDEDNESS IN NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS VIA t-SIMILARITY vol.24, pp.4, 2015, https://doi.org/10.11568/kjm.2016.24.4.723