Asymptotic stability for a homogeneous singularly perturbed system of differential equations with unbounded delay
Hristo Dimitrov Voulov; Drumi Dimitrov Bainov
Annales de la Faculté des sciences de Toulouse : Mathématiques (1993)
- Volume: 2, Issue: 1, page 97-116
- ISSN: 0240-2963
Access Full Article
topHow to cite
topDimitrov Voulov, Hristo, and Dimitrov Bainov, Drumi. "Asymptotic stability for a homogeneous singularly perturbed system of differential equations with unbounded delay." Annales de la Faculté des sciences de Toulouse : Mathématiques 2.1 (1993): 97-116. <http://eudml.org/doc/73315>.
@article{DimitrovVoulov1993,
author = {Dimitrov Voulov, Hristo, Dimitrov Bainov, Drumi},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {equiasymptotic stability; homogeneous singularly perturbed system of differential equations with unbounded delay},
language = {eng},
number = {1},
pages = {97-116},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Asymptotic stability for a homogeneous singularly perturbed system of differential equations with unbounded delay},
url = {http://eudml.org/doc/73315},
volume = {2},
year = {1993},
}
TY - JOUR
AU - Dimitrov Voulov, Hristo
AU - Dimitrov Bainov, Drumi
TI - Asymptotic stability for a homogeneous singularly perturbed system of differential equations with unbounded delay
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1993
PB - UNIVERSITE PAUL SABATIER
VL - 2
IS - 1
SP - 97
EP - 116
LA - eng
KW - equiasymptotic stability; homogeneous singularly perturbed system of differential equations with unbounded delay
UR - http://eudml.org/doc/73315
ER -
References
top- [1] Barnea ( B.I.) .— A method and new results for stability and instability of autonomous functional differential equations, SIAM J. Appl. Math.17 (1969), pp. 681-697. Zbl0181.10102MR254383
- [2] Cooke ( K.L.) .— The condition of regular degeneration for singularly perturbed linear differential-difference equations, J. Differential Equations1 (1965), pp. 39-94. Zbl0151.10303MR171977
- [3] Cooke ( K.L.) and Meyer ( K.R.) .— The condition of regular degeneration for singularly perturbed systems of linear differential-difference equations, J. Math. Anal. Appl.14 (1966), pp. 83-106. Zbl0142.05802MR190489
- [4] Driver ( R.D.) .— Existence and stability of solutions of a delay-differential system, Arch. Rat Mech. Anal.10 (1962), pp. 401-426. Zbl0105.30401MR141863
- [5] Halanay ( A.) .— Singular perturbations of systems with retarded argument, Rev. Math. Pures Appl.7 (1962). Zbl0133.33503MR178208
- [6] Hale ( J.K.) and Kato ( J.) .— Phase space for retarded differential equations with infinite delay, Funk. Ekvac.21 (1978), pp. 11-41. Zbl0383.34055MR492721
- [7] Hoppensteadt ( F.C.) .— Singular perturbations on the infinite interval, Trans. Amer. Math. Soc.123 (1966), pp. 521-525. Zbl0151.12502MR194693
- [8] Kato ( J.) .— Stability problem in functional differential equations with infinite delay, Funk. Ekvac.21 (1978), pp. 63-80. Zbl0413.34076MR492740
- [9] Klimushev ( A.I.) .— On asymptotic stability of systems with after-effect containing a small parameter as coefficient of the derivative, Prikl. Mat. Meh.26 (1962), pp. 52-61. Translated as J. Appl. Math. Mech.26 (1962), pp. 68-81. Zbl0108.08402MR145154
- [10] Krasovskii ( N.N.) .— Some problems in the theory of stability of motion, Moscow, 1959. English translation by J. Brenner, Stanford, California, 1962.
- [11] Lakshmikantham ( V.) and Leela ( S.) .— A unified approach to stability theory for differential equations with infinite delay, J. Int. Eqns10 (1985), pp. 147-156. Zbl0583.34058MR831241
- [12] Magalhaes ( L.T.) .— Convergence and boundary layers in singularly perturbed linear functional differential equations, J. Diff. Eqns54 (1984), pp. 295-309. Zbl0561.34060MR760374
- [13] Magalhaes ( L.T.) . — Exponential estimates for singularly perturbed functional differential equations, J. Math. Anal. Appl.103 (1984), pp. 443-460. Zbl0588.34052MR762568
- [14] Magalhaes ( L.T.) . — The asymptotics of solutions of singularly perturbed functional differential equations : distributed and concentrated delays are different, J. Math. Anal. Appl.105 (1985), pp. 250-257. Zbl0596.34051MR773586
- [15] Razumikhin ( B.S.) .— Application of Lyapunov's method to problems in the stability of systems with a delay, Automat. and Remote Control21 (1960), pp. 515-520. Zbl0114.04502
- [16] Rouche ( N.), Habets ( P.) and Laloy ( M.) .— Stability theory by Liapunov's direct method, Springer Verlag, 1977. Zbl0364.34022MR450715
- [17] Sawano ( K.) .— Exponentially asymptotic stability for functional differential equations with infinite retardations, Tohoku Math. J.31 (1979), pp. 363-382. Zbl0449.34053MR547651
- [18] Voulov ( H.D.) and Bainov ( D.D.) .— Asymptotic stability of singularly perturbed linear system with unbounded delay, Differential Equations : Qualitative Theory, Vol. I, II (Szeged, 1984), pp. 1097-1124. Colloq. Maht. Soc. Janos Bolyai, North Holland, 47 (1987). Zbl0622.34081MR890594
- [19] Voulov ( H.D.) and Bainov ( D.D.) .— On the asymptotic stability of differential equations with "maxima", Rend. Circ. Mat. Palermo, Serie II, Tomo XL (1991), pp. 385-420. Zbl0766.34054MR1174239
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.