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Oscillation of second order neutral differential equations

Published online by Cambridge University Press:  17 April 2009

L.H. Erbe  and
B.G. Zhang
L.H. Erbe
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
B.G. Zhang
Affiliation:
Shandong College of Oceanography, Qingdao, China
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Abstract

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Some new sufficient conditions are obtained for the oscillation of the neutral differential equation

where r(t) > 0, 0 < c < 1, p(t) ≥ 0, σ(t) > τ > 0 and α = 1 or 0 < α < 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 1 , February 1989 , pp. 71 - 80
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Bainov, D.D. and Zahariev, A.I., ‘Oscillating properties of the solutions of a class of neutral type functional differential equations’, Bull. Austral. Math. Soc. 22 (1980), 365–372.Google Scholar
[2]Bainov, D.D. and Zahariev, A.I., ‘Oscillating and asymptotic properties of a class of functional differential equations with maxima’, Czechoslovak Math. J. 34 (1984), 247–251.Google Scholar
[3]Erbe, L., ‘Oscillation criteria for second order nonlinear delay equations’, Canad. Math. Bull 18 (1973), 49–56.Google Scholar
[4]Grace, S.R. and Lalli, B.S., ‘Oscillation of nonlinear second order neutral delay differential equations’, Rad. Mat. 3 (1987), 77–84.Google Scholar
[5]Grammatikopoulos, M.K., Ladas, G. and Meimaridou, A., ‘Oscillations of second order neutral delay diffential equations’, Rad. Mat. 1 (1985), 267–274.Google Scholar
[6]Grammatikopoulos, M.K., Grove, E.A. and Ladas, G., ‘Oscillation and asymptotic behaviour of second order neutral differential equations.’, International Conference of Differential Equations at Univ. of Toronto, July 14–16.Google Scholar
[7]Ladas, G. and Sficas, Y.G., ‘Oscillations of higher-order neutral equations’, J. Austral. Math. Soc. 27 Ser. B (1986), 502–511.CrossRefGoogle Scholar
[8]Ladas, G., Partheniadis, E.C. and Sficas, Y.G., ‘Necessary and sufficient conditions for oscillation of second order neutral equation’, (preprint).Google Scholar
[9]Ladde, G.S., Lakshmikanthan, V. and Zhang, B.G., Oscillation theory of differential equations with deviating arguments (Marcel Dekker, New York, Basel, 1987).Google Scholar