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  • The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, Volume 27, Issue 4
  • April 1986, pp. 502-511

Oscilations of higher-order neutral equations

  • G. Ladas (a1) and Y. G. Sficas (a2)
  • DOI: http://dx.doi.org/10.1017/S0334270000005105
  • Published online: 01 February 2009
Abstract
Abstract

Sufficient conditions are given for the occurrence of various types of asymptotic behaviour in the solution of a class of n th order neutral delay differential equations. The conditions are in the form of certain inequalities amongst the constants involved in the definition of the differential equations, and specify either oscillatory behavior, or asymptotic divergence, or solutions which converge to zero.

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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. Bellman and K. L. Cooke , Differential-difference equations (Academic Press, New York, 1963).

[2]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.

[3]R. D. Driver , “Existence and continuous dependence of solutions of a neutral functional-differential equation”, Arch. Rational Mech. Anal. 19 (1965), 149166.

[4]R. D. Driver , “A mixed neutral system”, Nonlinear Anal.-TMA 8 (1984), 155158.

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

[8]G. Ladas and I. P. Stavroulakis , “On delay differential inequalities of higher order”, Canad. Math. Bull. 25 (1982), 348354.

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

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