DOI QR코드

DOI QR Code

BS-STABILITIES AND $\rho$-STABILITIES FOR FUNCTIONAL DIFFERENCE EQUATIONS WITH INFINITE DELAY

  • Choi, Sung Kyu (Department of Mathematics Chungnam National University) ;
  • Goo, Yoon Hoe (Department of Mathematics Hanseo University) ;
  • Im, Dong Man (Department of Mathematics Education Cheongju University) ;
  • Koo, Namjip (Department of Mathematics Chungnam National University)
  • Published : 2012.11.15

Abstract

We study the BS-stability and the $\rho$-stability for functional difference equations with infinite delay as a discretization of Murakami and Yoshizawa's results [6] for functional differential equation with infinite delay.

Keywords

References

  1. S. K. Choi, Y. H. Goo, D. M. Im, and N. Koo, Total stability in nonlinear discrete Volterra equations with unbounded delay, Abstr. Appl. Anal., Vol. 2009, ID 976369, 13 pages.
  2. S. K. Choi, Y. H. Goo, D. M. Im, and N. Koo, Stability and existence of almost periodic solutions of discrete Volterra equations with unbounded delay, J. Chungcheong Math. Soc. 24 (2011), 561-568.
  3. Y. Hamaya, Relationships between BC-s.d. ${\Omega}­(f)$ and (K, ${\rho}$)-s.d. ${\Omega­}(f)$ in a functional difference equation with infinite delay, Int. J. Difference Equ. 4 (2002), 303-321.
  4. Y. Hamaya, Existence of an almost periodic solution in a difference equation with infinite delay, J. Difference Equ. Appl. 9 (2003), 227-237. https://doi.org/10.1080/1023619021000035836
  5. Y. Hino, S. Murakami, and T. Naito, Functional Differential Equations with Infinite Delay, Springer-Verlag, New York, 1991.
  6. S. Murakami and T. Yoshizawa, Relationships between BC-stabilities and $\rho$-stabilities in functional differential equations with infinite delay, Tohoku Math. J. 44 (1992), 45-57. https://doi.org/10.2748/tmj/1178227375