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Oscillatory and asymptotic behaviour of all solutions of differential equations with deviating arguments†

Published online by Cambridge University Press:  14 November 2011

Ch. G. Philos
Ch. G. Philos
Affiliation:
Department of Mathematics, University of Ioannina, Greece
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Synopsis

This paper deals with the oscillatory and asymptotic behaviour of all solutions of a class of nth order (n > 1) non-linear differential equations with deviating arguments involving the so called nth order r-derivative of the unknown function x defined by

where r1, (i = 0,1,…, n – 1) are positive continuous functions on [t0, ∞). The results obtained extend and improve previous ones in [7 and 15] even in the usual case where r0 = r1 = … = rn–1 = 1.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 81 , Issue 3-4 , 1978 , pp. 195 - 210
Copyright
Copyright © Royal Society of Edinburgh 1978

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