DOI QR코드

DOI QR Code

BOUNDEDNESS IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS

  • Received : 2013.05.28
  • Accepted : 2013.07.18
  • Published : 2013.08.15

Abstract

In this paper, we investigate bounds for solutions of perturbed nonlinear differential systems.

Keywords

References

  1. F. Brauer, Perturbations of nonlinear systems of differential equations II, J. Math. Anal. Appl. 17 (1967), 579-591.
  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. S. K. Choi, N. J. Koo, and S. M. Song, Lipschitz stability for nonlinear functional differential systems, Far East J. Math. Sci(FJMS)I 5 (1999), 689-708.
  6. R. Conti, Sulla $t_{\infty}$-similitudine tra matricie l'equivalenza asintotica dei sistemi differenziali lineari, Rivista di Mat. Univ. Parma 8 (1957), 43-47.
  7. 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
  8. P. Gonzalez and M. Pinto, Stability properties of the solutions of the nonlinear functional differential systems, J. Math. Appal. 182 (1994), 562-573.
  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. Y . H. Goo, h-stability of the nonlinear differential systems, J. Chungcheong Math. Soc. 23 (2010), 383-389.
  11. V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications Vol. I, Academic Press, New York and London, 1969.
  12. M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), 161-175.
  13. M. Pinto, Stability of nonlinear differential systems, Applicable Analysis 43 (1992), 1-20. https://doi.org/10.1080/00036819208840049
  14. M. R. M. Rao and P. Srinivas, Asymptotic behavior of solutions of Volterra integro-differential equations, Proc. Amer. Math. Soc. 94 (1985), 55-60.

Cited by

  1. LIPSCHITZ AND ASYMPTOTIC STABILITY FOR PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS vol.21, pp.1, 2014, https://doi.org/10.7468/jksmeb.2014.21.1.11
  2. BOUNDEDNESS IN PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS VIA t∞-SIMILARITY vol.23, pp.2, 2015, https://doi.org/10.11568/kjm.2015.23.2.269
  3. BOUNDEDNESS IN NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS VIA t∞-SIMILARITY vol.24, pp.4, 2016, https://doi.org/10.11568/kjm.2016.24.4.723
  4. BOUNDEDNESS IN THE FUNCTIONAL NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS vol.22, pp.2, 2015, https://doi.org/10.7468/jksmeb.2015.22.2.101
  5. BOUNDEDNESS IN THE NONLINEAR FUNCTIONAL DIFFERENTIAL SYSTEMS vol.30, pp.4, 2015, https://doi.org/10.4134/CKMS.2015.30.4.415
  6. BOUNDEDNESS IN PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS vol.32, pp.5_6, 2014, https://doi.org/10.14317/jami.2014.697
  7. BOUNDEDNESS IN FUNCTIONAL PERTURBED DIFFERENTIAL SYSTEMS vol.28, pp.4, 2015, https://doi.org/10.14403/jcms.2015.28.4.499
  8. LIPSCHITZ AND ASYMPTOTIC STABILITY FOR NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS vol.27, pp.4, 2014, https://doi.org/10.14403/jcms.2014.27.4.591
  9. h-STABILITY AND BOUNDEDNESS IN FUNCTIONAL PERTURBED DIFFERENTIAL SYSTEMS vol.22, pp.2, 2015, https://doi.org/10.7468/jksmeb.2015.22.2.145
  10. BOUNDEDNESS IN THE PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS vol.27, pp.3, 2014, https://doi.org/10.14403/jcms.2014.27.3.479