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Some results on the asymptotic behavior of nonoscillatory solutions of differential equations with deviating arguments

Part of: Functional-differential and differential-difference equations Qualitative theory

Published online by Cambridge University Press:  09 April 2009

Ch. G. Philos ,
Y. G. Sficas  and
V. A. Staikos
Ch. G. Philos
Affiliation:
Department of Mathematics, University of Ioannina, Ioannina, Greece
Y. G. Sficas
Affiliation:
Department of Mathematics, University of Ioannina, Ioannina, Greece
V. A. Staikos
Affiliation:
Department of Mathematics, University of Ioannina, Ioannina, Greece
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Abstract

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This paper deals with some asymptotic properties of nonoscillatory solutions of a class of n-th order (n < 1) differential equations with deviationg arguments involving the so called n-th order r-derivative of the unknown function x defined by

where ri (i = 0,1…n) are positive continous functions on [t0, ∞). The fundamental purpose of this paper is to find for any integer m, 0 < m < n – 1, a necessary and sufficient condition (depending on m) in order that three exists at least one (nonoscillatory) solution x so that the exists in R – {0} The results obtained extend some recent ones due to Philos (1978a) and they prove, in a general setting, the validity of a conjecture made by Kusano and Onose (1975).

MSC classification

Secondary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory 34K25: Asymptotic theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 3 , June 1982 , pp. 295 - 317
Copyright
Copyright © Australian Mathematical Society 1982

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