h-STABILITY IN VOLTERRA DIFFERENCE SYSTEMS

  • Received : 2009.06.24
  • Accepted : 2009.08.14
  • Published : 2009.09.30

Abstract

We investigate h-stability of solutions of nonlinear Volterra difference systems and linear Volterra difference systems.

Keywords

Acknowledgement

Supported by : Hanseo University

References

  1. R. P. Agarwal, Difference Equations and Inequalities, Marcel Dekker Inc., New York, 1992.
  2. S. K. Choi and H. S. Ryu, h-stability in differential systems, Bull. Inst. Acad. Sinica. 21 (1993), 245-262.
  3. S. K. Choi and N. J. Koo, Stability in variation for nonlinear Volterra difference systems, Bull. Korean Math. Soc. 38 (2001), 101–111.
  4. S. K. Choi and N. J. Koo, Asymptotic equivalence between two linear Volterra difference systems, Comput. Math. Appl. 47 (2004), 461–471.
  5. 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.
  6. S. K. Choi , N. J. Koo and Y. H. Goo, Asymptotic property of nonlinear Volterra difference systems, Nonlinear Analysis. 51 (2002), 321–337.
  7. 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.
  8. S. K. Choi , N. J. Koo and H. S. Ruy, Asymptotic equivalence between two difference systems, Comput. Math. Appl. 45 (2003), 1327–1337.
  9. 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.
  10. Y. H. Goo and D. H. Ry, h-stability for perturbed integro-differential systems, J. Chungcheong Math. Soc. 21 (2008), 511–517.
  11. S. Elaydi, Periodicity and stability of linear Volterra difference systems, J. Math. Anal. Appl. 181 (2009), 483–492.
  12. V. Lakshmikantham and D. Trigiante, Theory of Difference Equations with Applications to Numerical Analysis, Academic Press, New York, 1988.
  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.
  16. M. Zouyousefain and S. Leela, Stability results for nonlinear difference equations of Volterra type, Appl. Math. Compu. 36 (1990), 51-61. https://doi.org/10.1016/0096-3003(90)90074-D