Conditions for factorization of linear differential-difference equations

Klara R. Janglajew, Kim Galjamovich Valeev


The paper deals with a linear system of differential equations of the form

$$\frac{dX(t)}{dt} = A X(t) + \mu\sum_{k=1}^{n}A_k X(t+\tau_k)$$

with constant coefficients, a small parameter and complex deviating argument.

Sufficient conditions for factorizing of this system are presented. This conditions are obtained by construction of an integral manifold of solutions to the considered system.

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