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Strong and Quasistrong Disconjugacy

Published online by Cambridge University Press:  20 November 2018

David London  and
Binyamin Schwarz
David London
Affiliation:
Department of Mathematics Technion, I.I.T., Haifa Israel
Binyamin Schwarz
Affiliation:
Department of Mathematics Technion, I.I.T., Haifa Israel
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Abstract

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A complex linear homogeneous differential equation of the nth order is called strong disconjugate in a domain G if, for every n points z1,…, zn in G and for every set of positive integers, k1…, kl, k1 + … + kl = n, the only solution y(z) of the equation which satisfies

is the trivial one y(z) = 0. The equation y(n)(z) = 0 is strong disconjugate in the whole plane and for every other set of conditions of the form y(mk(zk) = 0, k = 1 , . . . , n, m1 ≤ m2... mn, there exist, in any given domain, points z1 , . . . , zn and nontrivial polynomials of degree smaller than n, which satisfy these conditions. An analogous results holds also for real disconjugate differential equations.

Keywords

34C10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 4 , 01 December 1982 , pp. 435 - 440
Copyright
Copyright © Canadian Mathematical Society 1982

References

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