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A classification of the solutions of a differential equation according to their asymptotic behaviour

Published online by Cambridge University Press:  14 November 2011

Uri Elias
Uri Elias
Affiliation:
Department of Mathematics, Carnegie-Mellon University, Pittsburgh, U.S.A.
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Synopsis

The solutions of the differential equation Lny + p(x)y = 0, where Lny = ρn(ρn−1 … (ρ1(ρ0y)′)′ …)′ and p(x) is of one sign, are classified according to their behaviour as x → ∞. The solution space is decomposed into disjoint, non-empty sets Sk, 0≦K≦n, such that (−1)n−kp(x)≦0. We study the growth properties and the density of the zeros of the solutions which belong to the different sets Sk, the structure of the sets and its connection with (k, n − k)-disfocality.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 1-2 , 1979 , pp. 25 - 38
Copyright
Copyright © Royal Society of Edinburgh 1979

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