Abstract:
We study the exponential dichotomy of solutions to the Cauchy problem for a subclass of linear autonomous systems of functional-differential equations of neutral type by reducing this problem to the same problem for a difference equation of the form $x_{n}=\Gamma x_{n-1}$ with a compact operator $\Gamma$, in Banach space. The spectrum of $\Gamma$ is described. The dichotomy of the solutions of the Cauchy problem is a consequence of the dichotomy of the spectrum. In a particular case, the result obtained provides a criterion for the dichotomy for a linear autonomous system of functional-differential equations of retarded type of general form.
Keywords:dichotomy of a linear autonomous system, Cauchy problem, system of functional-differential equations, functional-differential equation of retarded (neutral) type, Banach space, spectrum.
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