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A comparison theorem for functional differential equations

Published online by Cambridge University Press:  17 April 2009

Athanassios G. Kartsatos  and
Hiroshi Onose
Athanassios G. Kartsatos
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida, USA
Hiroshi Onose
Affiliation:
Department of Mathematics, Ibaraki University, Mito, Japan.
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Abstract

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In this paper, we study the oscillation of nth-order differential equations. Recently, Atkinson and the present authors studied (separately) the comparison properties of differential inequalities. Kartsatos treated the nth-order ordinary case and proposed several open problems.

The purpose of this paper is to answer one of them in the affirmative concerning more general functional differential equations. The result is that if under several conditions, the equation

is oscillatory for n even or a solution x(t) of (1) is oscillatory or for n odd, then this is also the case for the equation

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 3 , June 1976 , pp. 343 - 347
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Atkinson, F.V., “On second order differential inequalities”, Proc. Roy. Soc. Edinburgh Sect. A 72 (1972/1974), 102–127 (1975).Google Scholar
[2]Kartsatos, Athanassios G., “On nth-order differential inequalities”, J. Math. Anal. Appl. 52 (1975), 1–9.CrossRefGoogle Scholar
[3]Kartsatos, Athanassios G., “Recent results on oscillation of solutions of forced and perturbed nonlinear differential equations of even order”, Stability of dynamical systems (NSF-CMBS Conference, Mississippi State University, 1975, to appear).Google Scholar
[4]Кигурадзе, И.Т. [I.T. Kiguradze], “О колеблемости решений уравнения”” On the oscillation of solutions of the equation ], Mat. Sb. 65 (107) (1964), 172–187.Google Scholar
[5]Onose, Hiroshi, “A comparison theorem and the forced oscillation”, Bull. Austral. Math. Soc. 13 (1975), 13–19.CrossRefGoogle Scholar