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    Ahmed, Fatima N. Ahmad, Rokiah R. Din, Ummul K. S. and Noorani, Mohd S. M. 2014. Oscillations for Neutral Functional Differential Equations. The Scientific World Journal, Vol. 2014, p. 1.


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    Arino, O and Győri, I 1989. Necessary and sufficient condition for oscillation of a neutral differential system with several delays. Journal of Differential Equations, Vol. 81, Issue. 1, p. 98.


    Farrell, K 1989. Necessary and sufficient conditions for oscillation of neutral equations with real coefficients. Journal of Mathematical Analysis and Applications, Vol. 140, Issue. 1, p. 251.


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  • The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, Volume 28, Issue 3
  • January 1987, pp. 362-375

Necessary and sufficient condition for oscillations of neutral differential equations

  • M. R. S. Kulenović (a1) (a2), G. Ladas (a1) and A. Meimaridou (a1) (a3)
  • DOI: http://dx.doi.org/10.1017/S0334270000005452
  • Published online: 01 February 2009
Abstract
Abstract

Consider the neutral delay differential equation

where pR, τ ≥ 0, q1 > 0, σ1 ≥ 0, for i = 1, 2, …, k. We prove the following result.

Theorem. A necessary and sufficient condition for the oscillation of all solutions of Eq. (1) is that the characteristic equation

has no real roots.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]R. K. Brayton and R. A. Willoughby , “On the numerical integration of a symmetric system of difference-differential equations of neutral type”, J. Math. Anal. Appl. 18 (1967), 182189.

[4]J. Hale , Theory of functional differential equations, (Springer-Verlag, New York, 1977).

[6]G. Ladas , Y. G. Sficas and I. P. Stavroulakis , “Necessary and sufficient conditions for oscillations”, Amer. Math. Monthly 90 (1983), 637640.

[8]M. Slemrod and E. F. Infante , “Asymptotic stability criteria for linear systems of differential equations of neutral type and their discrete analogues”, J. Math. Anal. Appl. 38 (1972), 399415.

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