Stability processes of moving invariant manifolds in uncertain impulsive differential-difference equations

Gani Tr. Stamov

Mathematica Bohemica (2009)

  • Volume: 134, Issue: 1, page 67-76
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Stamov, Gani Tr.. "Stability processes of moving invariant manifolds in uncertain impulsive differential-difference equations." Mathematica Bohemica 134.1 (2009): 67-76. <http://eudml.org/doc/38074>.

@article{Stamov2009,
abstract = {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.},
author = {Stamov, Gani Tr.},
journal = {Mathematica Bohemica},
keywords = {moving invariant set; stability theory; uncertain impulsive differential-difference system; moving invariant set; stability theory},
language = {eng},
number = {1},
pages = {67-76},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stability processes of moving invariant manifolds in uncertain impulsive differential-difference equations},
url = {http://eudml.org/doc/38074},
volume = {134},
year = {2009},
}

TY - JOUR
AU - Stamov, Gani Tr.
TI - Stability processes of moving invariant manifolds in uncertain impulsive differential-difference equations
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 1
SP - 67
EP - 76
AB - 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.
LA - eng
KW - moving invariant set; stability theory; uncertain impulsive differential-difference system; moving invariant set; stability theory
UR - http://eudml.org/doc/38074
ER -

References

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  1. Bainov, D., Kostadinov, S., Nguyen, Van Min, Dichotomies and Integral Manifolds of Impulsive Differential Equations, SCT Publishing, Singapore (1994). (1994) 
  2. Bainov, D., Stamova, I. M., 10.1017/S1446181100011986, ANZIAM J. 42 (2001), 341-353. (2001) Zbl0980.93074MR1818254DOI10.1017/S1446181100011986
  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. (1998) MR1769790
  4. Lakshmikantham, V., Leela, S., Martynyuk, A. A., Stability Analysis of Nonlinear Systems, Marcel Dekker, New York (1989). (1989) Zbl0676.34003MR0984861
  5. Lakshmikantham, V., Leela, S., Martynyuk, A. A., Practical Stability of Nonlinear Systems, World Scientific Publishing, Singapore (1990). (1990) Zbl0753.34037MR1089428
  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. (1997), 79-83 Sivasundaram, S. (1997) Zbl0947.34039MR1479421
  7. Shendge, G. R., 10.1016/0022-247X(83)90110-5, J. Math. Anal. Appl. 95 (1983), 319-334. (1983) MR0716086DOI10.1016/0022-247X(83)90110-5
  8. Siljak, D. D., Ikeda, M., Ohta, Y., Parametic stability, Proccedings Universita di Genova-Ohio State University Joint Conference: Birkhauser (1991), 1-20. (1991) MR1125087
  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. (1999) MR1834207
  10. Stamov, G., Stability of moving conditionally manifolds for impulsive differential equations, Adv. Stud. Contemp. Math. (Kyungshang) 9 (2004), 99-107. (2004) MR2067833
  11. Stamov, G., Impulsive integro-differential equations and stability of moving invariant maniolds, Methods Appl. Anal. 14 (2007), 69-76. (2007) MR2392627
  12. Stamova, I., Stamov, G., 10.1016/S0377-0427(99)00385-4, J. Comput. Appl. Math. 130 (2001), 163-171. (2001) Zbl1022.34070MR1827978DOI10.1016/S0377-0427(99)00385-4
  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. (1997) 

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