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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.

Rank two solutions of the abstract Cauchy problem