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Oscillatory and asymptotic behaviour of solutions of a class of linear ordinary differential equations

Published online by Cambridge University Press:  14 November 2011

Takaŝi Kusano ,
Manabu Naito  and
Kyoko Tanaka
Takaŝi Kusano
Affiliation:
Department of Mathematics, Faculty of Science, Hiroshima University, 1-1-89 Higashi-Senda, Naka-Ku, Hiroshima, 730 Japan
Manabu Naito
Affiliation:
Department of Mathematics, Faculty of Science, Hiroshima University, 1-1-89 Higashi-Senda, Naka-Ku, Hiroshima, 730 Japan
Kyoko Tanaka
Affiliation:
Department of Mathematics, Faculty of Science, Hiroshima University, 1-1-89 Higashi-Senda, Naka-Ku, Hiroshima, 730 Japan
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Synopsis

The equation to be considered is

where pi(t), 0≦i≦n, and q(t) are continuous and positive on some half-line [a, ∞). It is known that (*) always has “strictly monotone” nonoscillatory solutions defined on [a, ∞), so that of particular interest is the extreme situation in which such strictly monotone solutions are the only possible nonoscillatory solutions of (*). In this paper sufficient conditions are given for this situation to hold for (*). The structure of the solution space of (*) is also studied.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 90 , Issue 1-2 , 1981 , pp. 25 - 40
Copyright
Copyright © Royal Society of Edinburgh 1981

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