Asymptotic stability for a homogeneous singularly perturbed system of differential equations with unbounded delay
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 2 (1993) no. 1, pp. 97-116. 
@article{AFST_1993_6_2_1_97_0,
     author = {Dimitrov Voulov, Hristo and Dimitrov Bainov, Drumi},
     title = {Asymptotic stability for a homogeneous singularly perturbed system of differential equations with unbounded delay},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {97--116},
     publisher = {Universit\'e Paul Sabatier},
     address = {Toulouse},
     volume = {Ser. 6, 2},
     number = {1},
     year = {1993},
     mrnumber = {1230707},
     zbl = {0772.34054},
     language = {en},
     url = {http://archive.numdam.org/item/AFST_1993_6_2_1_97_0/}
}
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
SP  - 97
EP  - 116
VL  - 2
IS  - 1
PB  - Université Paul Sabatier
PP  - Toulouse
UR  - http://archive.numdam.org/item/AFST_1993_6_2_1_97_0/
LA  - en
ID  - AFST_1993_6_2_1_97_0
ER  - 
%0 Journal Article
%A Dimitrov Voulov, Hristo
%A Dimitrov Bainov, Drumi
%T Asymptotic stability for a homogeneous singularly perturbed system of differential equations with unbounded delay
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 1993
%P 97-116
%V 2
%N 1
%I Université Paul Sabatier
%C Toulouse
%U http://archive.numdam.org/item/AFST_1993_6_2_1_97_0/
%G en
%F AFST_1993_6_2_1_97_0
Dimitrov Voulov, Hristo; 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, Série 6, Tome 2 (1993) no. 1, pp. 97-116. http://archive.numdam.org/item/AFST_1993_6_2_1_97_0/

[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. | MR | Zbl

[2] Cooke (K.L.) .- The condition of regular degeneration for singularly perturbed linear differential-difference equations, J. Differential Equations 1 (1965), pp. 39-94. | MR | Zbl

[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. | MR | Zbl

[4] Driver (R.D.) .- Existence and stability of solutions of a delay-differential system, Arch. Rat Mech. Anal. 10 (1962), pp. 401-426. | MR | Zbl

[5] Halanay (A.) .- Singular perturbations of systems with retarded argument, Rev. Math. Pures Appl. 7 (1962). | MR | Zbl

[6] Hale (J.K.) and Kato (J.) .- Phase space for retarded differential equations with infinite delay, Funk. Ekvac. 21 (1978), pp. 11-41. | MR | Zbl

[7] Hoppensteadt (F.C.) .- Singular perturbations on the infinite interval, Trans. Amer. Math. Soc. 123 (1966), pp. 521-525. | MR | Zbl

[8] Kato (J.) .- Stability problem in functional differential equations with infinite delay, Funk. Ekvac. 21 (1978), pp. 63-80. | MR | Zbl

[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. | MR | Zbl

[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. Eqns 10 (1985), pp. 147-156. | MR | Zbl

[12] Magalhaes (L.T.) .- Convergence and boundary layers in singularly perturbed linear functional differential equations, J. Diff. Eqns 54 (1984), pp. 295-309. | MR | Zbl

[13] Magalhaes (L.T.) . - Exponential estimates for singularly perturbed functional differential equations, J. Math. Anal. Appl. 103 (1984), pp. 443-460. | MR | Zbl

[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. | MR | Zbl

[15] Razumikhin (B.S.) .- Application of Lyapunov's method to problems in the stability of systems with a delay, Automat. and Remote Control 21 (1960), pp. 515-520. | MR | Zbl

[16] Rouche (N.), Habets (P.) and Laloy (M.) .- Stability theory by Liapunov's direct method, Springer Verlag, 1977. | MR | Zbl

[17] Sawano (K.) .- Exponentially asymptotic stability for functional differential equations with infinite retardations, Tohoku Math. J. 31 (1979), pp. 363-382. | MR | Zbl

[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). | MR | Zbl

[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. | MR | Zbl