Estimates for Solutions to One Class of Nonlinear Systems of Neutral Type with Several Delays
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 4, pp. 32-43 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a class of systems of nonlinear differential equations of neutral type with several delays. We obtain conditions of exponential stability of the zero solution and establish estimates characterizing exponential decay rate of solutions at infinity.
Keywords: systems of neutral type, several delays, exponential stability, Lyapunov–Krasovskii functional, estimates for solutions.
@article{VNGU_2014_14_4_a3,
     author = {G. V. Demidenko and I. I. Matveeva},
     title = {Estimates for {Solutions} to {One} {Class} of {Nonlinear} {Systems} of {Neutral} {Type} with {Several} {Delays}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {32--43},
     year = {2014},
     volume = {14},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2014_14_4_a3/}
}
TY  - JOUR
AU  - G. V. Demidenko
AU  - I. I. Matveeva
TI  - Estimates for Solutions to One Class of Nonlinear Systems of Neutral Type with Several Delays
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2014
SP  - 32
EP  - 43
VL  - 14
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VNGU_2014_14_4_a3/
LA  - ru
ID  - VNGU_2014_14_4_a3
ER  - 
%0 Journal Article
%A G. V. Demidenko
%A I. I. Matveeva
%T Estimates for Solutions to One Class of Nonlinear Systems of Neutral Type with Several Delays
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2014
%P 32-43
%V 14
%N 4
%U http://geodesic.mathdoc.fr/item/VNGU_2014_14_4_a3/
%G ru
%F VNGU_2014_14_4_a3
G. V. Demidenko; I. I. Matveeva. Estimates for Solutions to One Class of Nonlinear Systems of Neutral Type with Several Delays. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 4, pp. 32-43. http://geodesic.mathdoc.fr/item/VNGU_2014_14_4_a3/

[1] L. E. El'sgol'ts, S. B. Norkin, Introduction to the Theory and Application of Differential Equations with Deviating Arguments, Academic Press, New York–London, 1973

[2] G. V. Demidenko, I. I. Matveeva, “Asymptotic properties of solutions to delay differential equations”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 5:3 (2005), 20–28 (in Russian)

[3] G. V. Demidenko, I. I. Matveeva, “Stability of solutions to delay differential equations with periodic coefficients of linear terms”, Sib. Mat. J., 48:5 (2007), 824–836 | DOI

[4] Demidenko G. V., “Stability of Solutions to Linear Differential Equations of Neutral Type”, J. Anal. Appl., 7:3 (2009), 119–130

[5] G. V. Demidenko, T. V. Kotova, M. A. Skvortsova, “Stability of solutions to differential equations of neutral type”, J. Math. Sci., 186:3 (2012), 394–406 | DOI

[6] I. I. Matveeva, A. A. Shcheglova, “Some estimates of the solutions to time-delay differential equations with parameters”, J. Appl. Ind. Math., 5:3 (2011), 391–399 | DOI

[7] G. V. Demidenko, E. S. Vodopyanov, M. A. Skvortsova, “Estimates of solutions to the linear differential equations of neutral type with several delays of the argument”, J. Appl. Ind. Math., 7:4 (2013), 472–479 | DOI

[8] I. I. Matveeva, “Estimates of solutions to a class of systems of nonlinear delay differential equations”, J. Appl. Ind. Math., 7:4 (2013), 557–566 | DOI

[9] G. V. Demidenko, I. I. Matveeva, “On exponential stability of solutions to one class of systems of differential equations of neutral type”, J. Appl. Ind. Math., 8:4 (2014), 510–520 | DOI

[10] Demidenko G. V., Matveeva I. I., “Estimates for Solutions to Linear Systems of Neutral Type with Several Delays”, J. Anal. Appl., 12:1–2 (2014), 37–52

[11] J. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977

[12] D. G. Korenevskij, Stability of dynamical systems under random perturbations of parameters. Algebraic criteria, Nauk. dumka, Kiev, 1989 (in Russian)

[13] Kolmanovskii V. B., Myshkis A. D., Introduction to the Theory and Applications of Functional-Differential Equations, Mathematics and its Applications, 463, Kluwer Academic Publishers, Dordrecht, 1999

[14] Kharitonov V. L., Time-Delay Systems. Lyapunov Functionals and Matrices, Control Engineering, Birkhäuser/Springer, N.Y., 2013