Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 20, pp. 1-12.

Title: Exponential stability of solutions to  nonlinear time-varying
       delay systems of neutral type equations with periodic coefficients

Authors=: Inessa I. Matveeva (Sobolev Institute of Math., Novosibirsk, Russia)

Abstract:
 We consider a class of nonlinear time-varying delay systems of neutral type
 differential equations with periodic coefficients in the linear terms,
 $$\begin{aligned}
 \frac{d}{dt} y(t)
 &= A(t) y(t) + B(t) y(t-\tau(t)) + C(t) \frac{d}{dt} y(t-\tau(t)) \cr
 &\quad + F\Big(t, y(t), y(t-\tau(t)), \frac{d}{dt} y(t-\tau(t)) \Big),
 \end{aligned}$$
 where  A(t), B(t), C(t) are T-periodic matrices, and
 $$
 \|F(t,u,v,w)\| \le q_1\|u\| + q_2\|v\| + q_3 \|w\|,
 \quad  q_1, q_2,  q_3 \ge 0, \quad  t > 0.
 $$
 We obtain conditions for the exponential stability of the zero solution
 and estimates for the exponential decay of the solutions at infinity.
 
Submitted April 30, 2019. Published February 14, 2020.
Math Subject Classifications: 34K20.
Key Words: Time-varying delay equation; neutral equation; periodic coefficient;
           exponential stability.