On asymptotic stability in nonlinear differential system

  • 투고 : 2010.04.03
  • 심사 : 2010.05.03
  • 발행 : 2010.05.31

초록

We obtain, in using generalized norms, some stability results for a very general system of di erential equations using the method of cone-valued Lyapunov funtions and we obtain necessary and/or sufficient conditions for the uniformly asymptotic stability of the nonlinear differential system.

키워드

참고문헌

  1. Akpan, E. P. and Akinylee, O. (1992). On the $\phi_{0}$ -Stability of comparison differential systems. Journal of Math. Anal. and Appl., 164, 307-324. https://doi.org/10.1016/0022-247X(92)90116-U
  2. Brauer, F. (1965). Some refinements of Lyapunov's second method. Canadian Journal Math, 5, 811-819.
  3. Brauer, F. and Nohel, J. A. (1969). Qulitative theory of ordinary differential equations, Benjamin, New York.
  4. Danan, F. M. and Elaydi, S. (1969). Lipschitz stability of nonlinear systems of differential equations, II, Lyapunov function. Journal Math. Anal. Appl., 143, 517-529.
  5. Ki, H. (2000). Second order approximations to the stopping time with fixed proportional accuracy. Journal of the Korean Data & Information Science Society, 11, 103-110.
  6. Ladde, G. S. (1976). Competitive processes and comparison differential systems. Trans. Amer. Math. Soc., 221, 391-402. https://doi.org/10.1090/S0002-9947-1976-0407401-7
  7. Lakshmikantham, V. and Leela, S. (1969). Differential and integral inequalities, Thoery and Appl. Vol. I , Academic Press, New York.
  8. Lakshmikantham, V. and Leela, S. (1977). Cone-valued Lyapunov function. Journal Nonlinear Anal. Theory, Methods and Appl, 1, 215-222. https://doi.org/10.1016/0362-546X(77)90031-1
  9. Lakshmikantham, V., Leela, S. and Martynyuk, A. A. (1989). Stability analysis of nonlinear system, Marcel Dekker, Inc.
  10. Lakshmikantham, V., Matrosov, V. M. and Sivasundaram, S. (1991). Vector Lyapunov function and stability analysis of nonlinear systems, Klluwer Academic Publishers.
  11. Lee, I. S., Choi, J. K., Cho, K. H., Choi, D. W. and Jeong, S. H. (1999). Asymptotic relative efficiencies of the nonparametric relative, risk estimators for the two sample proportional hazard model. Journal of the Korean Data & Information Science Society, 10, 103-111.
  12. Lee, O. S. (2007). Sufficient conditions for stationarity of smooth transitio ARMA/GARCH models. Journal of the Korean Data & Information Science Society, 18, 237-245.
  13. Moon, K. A. and Shin, I. H. (1997). The asymptotic properties of mean residual life function on left truncated and right censoring model. Journal of the Korean Data & Information Science Society, 8, 99-110.