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

Abstract

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 \(L^p([0,\infty ), \mathbb {C}^n)\), has a solution belonging to \(L^p([0,\infty ), \mathbb {C}^n)\).