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Não disponívelWe are concerned with the following ordinary differential equation: (1) 5: : A(t)z + f(t,x), where :, x, f(t,x) are n-vectors, A(t) is an nxn matrix, the independent variable t ranging on [O,∞). A well known theorem of Corduneanu [5, Th. I] establishes the existence of a set f of solutions of (1), contained in a given Banach space D. Furthermore, f can be posed in one-to-one correspondence with a subspace of the phase space. This work is planned as follows: First, we study the admissibility of certains pairs of Banach spaces (B,D) with respect to A(t). In other words, we look for sufficient conditions in order that the (equation. (2) y = A(t)y + b(t) have a solution in D, provided b(t) ε B. Secondly, under suitable conditions we establish homeomorphisms between the above mentioned set f, its section f(0), and a subspace of the phase space. In the last part, we introduce the concept of D stability as an extension of stability in the sense of Lyapunov. We deal with admissibility results, in connection with the topological properties of the set f, to make applications in conditional Dstability. The main tool used here is prowided by results of Massera and Schãffer on linear differential equations and functional analysis [11,12,13]