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Extension of a Result of L. Lorch and P. Szego On Higher Monotonicity

Published online by Cambridge University Press:  20 November 2018

M. E. Muldoon
M. E. Muldoon*
Affiliation:
York University, Toronto
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We suppose that {x1, x2, …}, are increasing sequences of consecutive zeros of non-trivial solutions y(x), , of the differential equation

(1)

on an open interval I, and define, for any fixed λ > - 1,

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 3 , August 1968 , pp. 447 - 451
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Lorch, Lee and Szego, Peter, Higher monotonicity properties of certain Sturm-Liouville functions. Acta Math., 109 (1963) 55-73.Google Scholar
2. Lorch, Lee and Szego, Peter, Higher monotonicity properties of certain Sturm-Liouville functions II. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 11 (1963) 455-457.Google Scholar
3. Pólya, G. and Szegö, G., Aufgaben und Lehrsätze aus der Analysis II. (2nd ed., Berlin, 1954).Google Scholar
4. Seminar, D.E., Some elementary converse problems in ordinary differential equation (Seminar on differential equations, Aarhus University, 1964-65), to appear in Canadian Mathematical Bulletin.Google Scholar