Geodesic
Exponential stability of solutions to nonlinear time-delay systems of neutral type
Electronic journal of differential equations, Tome 2016 (2016)
We consider a nonlinear time-delay system of neutral equations with constant coefficients in the linear terms

$ \frac{d}{dt}\big(y(t) + D y(t-\tau)\big) = A y(t) + B y(t-\tau) + F(t, y(t), y(t-\tau)), $

where

$ \|F(t,u,v)\| \le q_1\|u\|^{1+\omega_1} + q_2\|v\|^{1+\omega_2}, \quad q_1, q_2, \omega_1, \omega_2 > 0. $

We obtain estimates characterizing the exponential decay of solutions at infinity and estimates for attraction sets of the zero solution.
Classification : 34K20
Keywords: time-delay systems, neutral equation, exponential stability, attraction sets 
@article{EJDE_2016__2016__a14,
     author = {Demidenko,  Gennadii V. and Matveeva,  Inessa I.},
     title = {Exponential stability of solutions to nonlinear time-delay systems of neutral type},
     journal = {Electronic journal of differential equations},
     year = {2016},
     volume = {2016},
     zbl = {1329.34116},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a14/}
}
TY  - JOUR
AU  - Demidenko,  Gennadii V.
AU  - Matveeva,  Inessa I.
TI  - Exponential stability of solutions to nonlinear time-delay systems of neutral type
JO  - Electronic journal of differential equations
PY  - 2016
VL  - 2016
UR  - http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a14/
LA  - en
ID  - EJDE_2016__2016__a14
ER  - 
%0 Journal Article
%A Demidenko,  Gennadii V.
%A Matveeva,  Inessa I.
%T Exponential stability of solutions to nonlinear time-delay systems of neutral type
%J Electronic journal of differential equations
%D 2016
%V 2016
%U http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a14/
%G en
%F EJDE_2016__2016__a14
Demidenko,  Gennadii V.; Matveeva,  Inessa I. Exponential stability of solutions to nonlinear time-delay systems of neutral type. Electronic journal of differential equations, Tome 2016 (2016). http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a14/