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Oscillations of Second Order Neutral Equations

Published online by Cambridge University Press:  20 November 2018

G. Ladas ,
E. C. Partheniadis  and
Y. G. Sficas
G. Ladas
Affiliation:
University of Rhode Island, Kingston, Rhode Island
E. C. Partheniadis
Affiliation:
University of Ioannina, Ioannina, Greece
Y. G. Sficas
Affiliation:
University of Ioannina, Ioannina, Greece
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Consider the second order neutral differential equation

1

where the coefficients p and q and the deviating arguments τ and σ are real numbers. The characteristic equation of Eq. (1) is

2

The main result in this paper is the following necessary and sufficient condition for all solutions of Eq. (1) to oscillate.

THEOREM. The following statements are equivalent:

  • (a) Every solution of Eq. (1) oscillates.

  • (b) Equation (2) has no real roots.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 6 , 01 December 1988 , pp. 1301 - 1314
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Grammatikopoulos, M. K., Grove, E. A. and Ladas, G., Oscillation and asymptotic behavior of second order neutral differential equations with deviating arguments, Proceedings of the International Conference in Differential Equations, Univ. of Toronto, Canada, July 14–26, 1986.Google Scholar
2. Ladas, G., Partheniadis, E. C. and Sficas, Y. G., Necessary and sufficient conditions for oscillations of second order neutral equations, J. Math. Anal. Appl. (to appear).CrossRefGoogle Scholar
3. Ladas, G., Partheniadis, E. C. and Sficas, Y. G., Oscillations of second order neutral equations, Proceedings of Equadiff 87, to be published by Marcel Dekker, Inc.CrossRefGoogle Scholar