Geodesic
Stability processes of moving invariant manifolds in uncertain impulsive differential-difference equations
Mathematica Bohemica, Tome 134 (2009) no. 1, pp. 67-76

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
We present a result on the stability of moving invariant manifolds of nonlinear uncertain impulsive differential-difference equations. The result is obtained by means of piecewise continuous Lyapunov functions and a comparison principle.
We present a result on the stability of moving invariant manifolds of nonlinear uncertain impulsive differential-difference equations. The result is obtained by means of piecewise continuous Lyapunov functions and a comparison principle.
DOI : 10.21136/MB.2009.140641
Classification : 34A37, 34K45
Keywords: moving invariant set; stability theory; uncertain impulsive differential-difference system 
Stamov, Gani Tr. Stability processes of moving invariant manifolds in uncertain impulsive differential-difference equations. Mathematica Bohemica, Tome 134 (2009) no. 1, pp. 67-76. doi: 10.21136/MB.2009.140641
@article{10_21136_MB_2009_140641,
     author = {Stamov, Gani Tr.},
     title = {Stability processes of moving invariant manifolds in uncertain impulsive differential-difference equations},
     journal = {Mathematica Bohemica},
     pages = {67--76},
     year = {2009},
     volume = {134},
     number = {1},
     doi = {10.21136/MB.2009.140641},
     mrnumber = {2504689},
     zbl = {1212.34225},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2009.140641/}
}
TY  - JOUR
AU  - Stamov, Gani Tr.
TI  - Stability processes of moving invariant manifolds in uncertain impulsive differential-difference equations
JO  - Mathematica Bohemica
PY  - 2009
SP  - 67
EP  - 76
VL  - 134
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2009.140641/
DO  - 10.21136/MB.2009.140641
LA  - en
ID  - 10_21136_MB_2009_140641
ER  - 
%0 Journal Article
%A Stamov, Gani Tr.
%T Stability processes of moving invariant manifolds in uncertain impulsive differential-difference equations
%J Mathematica Bohemica
%D 2009
%P 67-76
%V 134
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2009.140641/
%R 10.21136/MB.2009.140641
%G en
%F 10_21136_MB_2009_140641

[1] Bainov, D., Kostadinov, S., Nguyen, Van Min: Dichotomies and Integral Manifolds of Impulsive Differential Equations. SCT Publishing, Singapore (1994).

[2] Bainov, D., Stamova, I. M.: Vector Lyapunov functions and conditional stability for systems of impulsive differential-difference equations. ANZIAM J. 42 (2001), 341-353. | DOI | MR | Zbl

[3] Bainov, D., Dishliev, A. B., Stamova, I. M.: Continuous dependence of solutions of impulsive systems of differential-diference equations on initial data and on parameter. Bol. Soc. Parana. Mat. 18 (1998), 21-34. | MR

[4] Lakshmikantham, V., Leela, S., Martynyuk, A. A.: Stability Analysis of Nonlinear Systems. Marcel Dekker, New York (1989). | MR | Zbl

[5] Lakshmikantham, V., Leela, S., Martynyuk, A. A.: Practical Stability of Nonlinear Systems. World Scientific Publishing, Singapore (1990). | MR | Zbl

[6] Lakshmikantham, V., Vatsala, S. A.: Stability of moving invariant sets. Advances in Nonlinear Dynamics. Langhorne, PA: Cordon and Breach. Stab. Control Theory Methods Appl. {\it 5} (1997), 79-83 Sivasundaram, S. | MR | Zbl

[7] Shendge, G. R.: A new approach to the stability theory of functional differential equations. J. Math. Anal. Appl. 95 (1983), 319-334. | DOI | MR

[8] Siljak, D. D., Ikeda, M., Ohta, Y.: Parametic stability. Proccedings Universita di Genova-Ohio State University Joint Conference: Birkhauser (1991), 1-20. | MR

[9] Stamov, G.: Stability of moving invariant maniolds for impulsive differential equations. J. Tech. Univ. Plovdiv Fundam. Sci. Appl., Ser. A Pure Appl. Math. 7 (1999), 99-107. | MR

[10] Stamov, G.: Stability of moving conditionally manifolds for impulsive differential equations. Adv. Stud. Contemp. Math. (Kyungshang) 9 (2004), 99-107. | MR

[11] Stamov, G.: Impulsive integro-differential equations and stability of moving invariant maniolds. Methods Appl. Anal. 14 (2007), 69-76. | MR

[12] Stamova, I., Stamov, G.: Lyapunov-Razumikhin method for impulsive functional differential equations and applications to the population dynamics. J. Comput. Appl. Math. 130 (2001), 163-171. | DOI | MR | Zbl

[13] Vatsala, A. S., Deo, G. S.: Stability of moving invariant sets for functional differential systems. Int. J. Nonlin. Diff. Eq.: Theory, Methods and Appl. 3 (1997), 179-186.

Cité par Sources :