Abstract:
In the present paper we study stability of solutions to systems
of quasi-linear delay differential equations of neutral type
ddt(y(t)+Dy(t−τ))=Ay(t)+By(t−τ)+F(t,y(t),y(t−τ)),t>τ,
where
A, B, D
are n×n numerical matrices,
τ>0 is a delay parameter,
F(t,u,v)
is a real-valued vector-function satisfying Lipschitz condition
with respect to
u
and
F(t,0,0)=0.
Stability conditions of the zero solution to the systems are obtained,
uniform estimates for the solutions on the half-axis
{t>τ} are established.
In the case of asymptotic stability these estimates give
the decay rate of the solutions at infinity.
Keywords:
quasi-linear differential equations of neutral type, asymptotic stability, attraction domain, uniform estimates for solutions, modified Lyapunov–Krasovskii functional.
Citation:
G. V. Demidenko, T. V. Kotova, M. A. Skvortsova, “Stability of solutions to differential equations of neutral type”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 10:3 (2010), 17–29; J. Math. Sci., 186:3 (2012), 394–406
\Bibitem{DemKotSkv10}
\by G.~V.~Demidenko, T.~V.~Kotova, M.~A.~Skvortsova
\paper Stability of solutions to differential equations of neutral type
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2010
\vol 10
\issue 3
\pages 17--29
\mathnet{http://mi.mathnet.ru/vngu47}
\transl
\jour J. Math. Sci.
\yr 2012
\vol 186
\issue 3
\pages 394--406
\crossref{https://doi.org/10.1007/s10958-012-0994-x}
Linking options:
https://www.mathnet.ru/eng/vngu47
https://www.mathnet.ru/eng/vngu/v10/i3/p17
This publication is cited in the following 10 articles:
Yener Altun, “Stability estimates for a class of neutral type systems with distributed time-varying delay components”, Adv Cont Discr Mod, 2025:1 (2025)
G. V. Demidenko, I. I. Matveeva, Springer Proceedings in Mathematics & Statistics, 379, Functional Differential Equations and Applications, 2021, 145
T. Yskak, “Stability of Solutions to One Class of Neutral Type Systems of Linear Autonomous Equations with Distributed Delay”, Lobachevskii J Math, 42:14 (2021), 3561
T. Yskak, “On the stability of systems of linear differential equations of neutral type with distributed delay”, J. Appl. Industr. Math., 13:3 (2019), 575–583
G. V. Demidenko, I. I. Matveeva, M. A. Skvortsova, “Estimates for solutions to neutral differential equations with periodic coefficients of linear terms”, Siberian Math. J., 60:5 (2019), 828–841
G. V. Demidenko, I. I. Matveeva, “O robastnoi ustoichivosti reshenii lineinykh differentsialnykh uravnenii neitralnogo tipa s periodicheskimi koeffitsientami”, Sib. zhurn. industr. matem., 18:4 (2015), 18–29
G. V. Demidenko, I. I. Matveeva, “On the exponential stability of solutions to one class of differential equations of neutral type”, J. Appl. Industr. Math., 8:4 (2014), 510–520
G. V. Demidenko, I. I. Matveeva, “Estimates for Solutions to One Class of Nonlinear Systems of Neutral Type with Several Delays”, J. Math. Sci., 213:6 (2016), 811–822
M. A. Skvortsova, “Asymptotic Properties of Solutions to Systems of Differential Equations of Neutral Type in Time-Varying Delay Case”, J. Math. Sci., 205:3 (2015), 455–463
M. A. Skvortsova, “Otsenki reshenii i oblasti prityazheniya nulevogo resheniya sistem kvazilineinykh uravnenii neitralnogo tipa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2011, no. 10, 30–39