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Limit Point Criteria for Differential Equations

Published online by Cambridge University Press:  20 November 2018

Don Hinton
Don Hinton*
Affiliation:
The University of Tennessee, Knoxville, Tennessee
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For certain ordinary differential operators L of order 2n, this paper considers the problem of determining the number of linearly independent solutions of class L2[a, ∞) of the equation L(y) = λy. Of central importance is the operator

0.1

where the coefficients pi are real. For this L, classical results give that the number m of linearly independent L2[a, ∞) solutions of L(y) = λy is the same for all non-real λ, and is at least n [10, Chapter V]. When m = n, the operator L is said to be in the limit-point condition at infinity. We consider here conditions on the coefficients pi of L which imply m = n. These conditions are in the form of limitations on the growth of the coefficients.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 2 , April 1972 , pp. 293 - 305
Copyright
Copyright © Canadian Mathematical Society 1972

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