Estimates for solutions to a class of nonautonomous systems of neutral type with unbounded delay
The paper deals with nonlinear systems of nonautonomous differential equations of neutral type with unbounded delay of the form \[ \frac{d}{dt} y(t)= A(t)\,y(t)+ B(t)\, y(t-\tau(t))+C(t)\, \frac{d}{dt} y(t-\tau(t))\] \[\\ \quad + F\left(t,y(t),y(t-\tau(t)), \frac{d}{dt} y(t-\tau(t)\right)\,,\; t\geq 0\,.\] By means of appropriate Lyapunov-Krasovskii functionals, the author studies the stability of solutions, first for the linear case, and then for some nonlinear ones when \(\|F(t,u,v,w)\|\leq q\, \|u\|^{1+w}\) with \(w\geq 0\). In the particular case of exponential and asymptotic stability, some estimates about the attraction domain are obtained.
scientific article; zbMATH DE number 7356189
scientific article