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Solution Space Decompositions for nth Order Linear Differential Equations

Published online by Cambridge University Press:  20 November 2018

G. B. Gustafson  and
S. Sedziwy
G. B. Gustafson
Affiliation:
University of Utah, Salt Lake City, Utah
S. Sedziwy
Affiliation:
University of Utah, Salt Lake City, Utah
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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).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 3 , 01 June 1975 , pp. 508 - 512
Copyright
Copyright © Canadian Mathematical Society 1975

References

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