Consider the wth order scalar ordinary differential equation
∈ C([0, ∞) → R ) . The purpose of this paper is to establish the following:
DECOMPOSITION THEOREM. The solution space X of (1.1) has a direct sum Decomposition
where M1 and M2 are subspaces of X such that
(1) each solution in M1\﹛0﹜ is nonzero for sufficiently large t ﹛nono sdilatory) ;
(2) each solution in M2 has infinitely many zeros ﹛oscillatory).