Introduction

Abstract

Complete second order linear differential equations in Banach spaces

$$y''(t) + Ay'(t) + By(t) = 0$$

((1))

have been extensively studied during the last thirty-five years. Nevertheless, as H.O. Fattorini remarked in the monograph “Second order linear differential equations in Banach spaces” (1985): “The theory of (1) is considerably more complicated than that of its incomplete counterpart $y''(t) + By(t) = 0$ and can hardly be said to be in definitive form” [93. p. 270].