The Abel equation in the asymptotic theory of functional differential equations (Q1849454)

The author studies the asymptotic behaviour of the solutions of the matrix delay differential equation \[ \dot {\mathbf x} (t) = {\mathbf {A x}} (\tau (t)) + {\mathbf {Bx}} (t) \quad t \in [t_0, \infty) \] with complex constant matrices \textbf{A,\ B} and \( \tau \) a real-valued function satisfying certain regularity conditions. Relations with the Abel equation \( \varphi ( \tau (t)) = \varphi (t) - 1 \) are given.