On Semigroups in Rn X Lp Corresponding to Differential Equations with Delays

Abstract

In this paper we study some properties of the semigroups associated with the linear retarded functional differential equations (FDE) in the setting of Banach spaces Rⁿ X L^p( — h, 0, Rⁿ), 1 < p < ∞. Earlier investigations of these equations via semigroups defined on the customary space C([ — h, 0], Rⁿ) played an important role in problems of stability, oscillations, bifurcation, asymptotic behavior etc. [15].