Rank two solutions of the abstract Cauchy problem

Abstract

In this paper we discuss solutions of the Abstract Cauchy Problem

Bu(α) (t) = Au(t)+ f (t)

u(0) = x0

that are of the form u = u1⊗δ1+u2⊗δ2 , where u and f are functions defined on [0,a] with values in the Hilbert space l2.