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Strongly Oscillatory and Nonoscillatory Subspaces of Linear Equations

Published online by Cambridge University Press:  20 November 2018

J. Michael Dolan  and
Gene A. Klaasen
J. Michael Dolan
Affiliation:
Oak Ridge National Laboratory, Operated by Union Carbide Corporation for the U.S. Atomic Energy Commission, Oak Ridge, Tennessee
Gene A. Klaasen
Affiliation:
University of Tennessee, Knoxville, Tennessee
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Consider the nth order linear equation

and particularly the third order equation

A nontrivial solution of (1)n is said to be oscillatory or nonoscillatory depending on whether it has infinitely many or finitely many zeros on [a, ∞). Let denote respectively the set of all solutions, oscillatory solutions, nonoscillatory solutions of (1)n. is an n-dimensional linear space. A subspace is said to be nonoscillatory or strongly oscillatory respectively if every nontrivial solution of is nonoscillatory or oscillatory. If contains both oscillatory and nonoscillatory solutions then is said to be weakly oscillatory.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 1 , 01 February 1975 , pp. 106 - 110
Copyright
Copyright © Canadian Mathematical Society 1975

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