Geodesic
Solution Space Decompositions for nth Order Linear Differential Equations
Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 508-512

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Consider the wth order scalar ordinary differential equation with pr ∈ 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). 
Gustafson, G. B.; Sedziwy, S. Solution Space Decompositions for nth Order Linear Differential Equations. Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 508-512. doi: 10.4153/CJM-1975-062-x
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