Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T02:53:20.705Z Has data issue: false hasContentIssue false

A classification of the solutions of a differential equation according to their behaviour at infinity, II

Published online by Cambridge University Press:  14 November 2011

Uri Elias
Affiliation:
Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel

Synopsis

The solutions of the differential equation Lny + p(×)y = 0, where Ln is a disconjugate operator, are classified according to their behaviour as × →∞. The solution space is decomposed into disjoint sets. We study the dominance properties of the solutions which belong to different sets.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Elias, U.. A classification of the solutions of a differential equation according to their asymptotic behaviour. Proc. Roy. Soc. Edinburgh Sect. A 83 (1979), 2538.CrossRefGoogle Scholar
2Etgen, G. J. and Taylor, W. E.. The essential uniqueness of bounded nonoscillatory solutions of certain even order differential equations. Pacific J. Math. 68 (1977), 339346.CrossRefGoogle Scholar
3Jones, G. D.. An ordering of oscillation types for y (n) + py=0. SIAM J. Math. Anal. 12 (1981), 7277.CrossRefGoogle Scholar
4Karlin, S.. Total positivity (Stanford University Press, 1968).Google Scholar
5Kim, W. J.. Properties of disconjugate linear differential operators. J. Differential Equations 43 (1982), 369398.CrossRefGoogle Scholar
6Kitamura, Y. and Kusano, T.. Nonlinear oscillation of higher order functional differential equations with deviating arguments. J. Math. Anal. Appl. 77 (1980), 100119.CrossRefGoogle Scholar
7Nehari, Z.. Green's functions and disconjugacy. Arch. Rational Mech. Anal. 62 (1976), 5376.CrossRefGoogle Scholar
8Nehari, Z.. Disconjugate differential operators. Trans. Amer. Math. Soc. 129 (1967), 500516.CrossRefGoogle Scholar
9Trench, W. F.. Canonical forms and principal systems for general disconjugate equations. Trans. Amer. Math. Soc. 189 (1974), 319327.CrossRefGoogle Scholar