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The Abel equation in the asymptotic theory of functional differential equations. (English) Zbl 1010.39007

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 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.

MSC:

39B22 Functional equations for real functions
39B72 Systems of functional equations and inequalities
34K25 Asymptotic theory of functional-differential equations
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