Stability of solutions to differential equations with several variable delays. II (Q384249)

Consider the family of equations \[ \dot{x}(t)=a_0x(t)-\sum_{k=1}^n a_k x(t-r_k(t)),\, t\geq 0 \] for different fixed sets of parameters \(p=\{a_0, a_1, \dots a_n, \omega_1, \dots, \omega_n\}\), where \(a_0 \in \mathbb{R}\), \(a_k, \omega_k >0\) and \(r_k:[0,\infty) \rightarrow [0,\omega_k ]\), \(k=\overline{1,n}\). The main results of the paper give criteria for sign definiteness and asymptotic, uniform and exponential stability. For Part I see [the authors, Russ. Math. 57, No. 6, 21--31 (2013); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2013, No. 6, 25-36 (2013; Zbl 1288.34063)].