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A proof of characterisation of oscillation for higher-order neutral differential equations of mixed type by the Laplace transform

Published online by Cambridge University Press:  14 November 2011

O. Arino  and
M. A. El Attar
O. Arino
Affiliation:
Département de Mathématiques, Université de Pau, 64000 Pau, France
M. A. El Attar
Affiliation:
Department of Mathematics, University of Tanta, Tanta, Egypt
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Extract

Consider the general expression of such equations in the form

where Ai, Bj, ∊ ℝ, δo = 0 dn/ 0, dn are n-derivatives, n ≧ l, the σj'S and δj,'s respectively, are ordered as an increasing family with possibly positive and negative terms. These are the deviating arguments. In this paper, we provide a proof of this result based on the use of the Laplace transform. Our method involves new results regarding the exponential growth of positive solutions for such equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 5 , 1994 , pp. 909 - 916
Copyright
Copyright © Royal Society of Edinburgh 1994

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References

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