The L~p-Version of the Generalized Bohl–Perron Principle for Neutral Type Functional Differential Equations

摘要

We consider a vector linear neutral type homogeneous functional differential equation. It is proved that the considered equation is exponentially stable, provided the corresponding non-homogeneous equation with the zero initial function and an arbitrary free term from L~p([0,∞),C~n), has a solution belonging to L~p([0,∞),C~n).