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Oscillation and nonoscillation of a delay differential equation

  • Chunhai Kou (a1) (a2), Weiping Yan (a2) and Jurang Yan (a2)

Abstract

In this paper, some necessary and sufficient conditions for oscillation of a first order delay differential equation with oscillating coefficients of the form

are established. Several applications of our results improve and generalise some of the known results in the literature.

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References

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[1]Chen, Yongshao, ‘Oscillation and asymptotic behavior of solutions of first order linear functional differential equations with oscillatory coefficients’, (in Chinese), Acta Math. Appl. Sinica 12 (1989), 96104.
[2]Györi, I. and Ladas, G., Oscillation theory of delay differential equations with applications (Clarendon Press, Oxford, 1991).
[3]Hunt, B.R. and Yorke, J.A., ‘When all solutions of oscillate’, J. Differential Equations 53 (1984), 139145.
[4]Koplatadze, R.G. and Chanturia, T.A., ‘On the oscillatory and monotone solutions of first order differential equations with deviating arguments’, (in Russian), Differensial'nye Uravneniya 18 (1982), 14631465.
[5]Kulenovic, M.R. and Grammatikopoulos, M.K., ‘First order functional differential inequalities with oscillating coefficients’, Nonlinear Anal. 8 (1984), 10431054.
[6]Kulenovic, M.R. and Grammatikopoulos, M.K., ‘Some comparison and oscillation results for first order differential equations and inequalities with a deviating argument’, J. Math. Anal. Appl. 131 (1988), 6784.
[7]Kwong, M.K., ‘Oscillation of first order delay equations’, J. Math. Anal. Appl. 156 (1991), 274286.
[8]Ladas, G., Sficas, Y.G. and Stavroulakis, I.P., ‘Functional differential inequalities and equations with oscillating coefficients’, in Trends in theory and practice of nonlinear differential equations, (Lakshmikantham, V., Editor) (Marcel Dekker, New York, Basel, 1984).
[9]Yu, J.S., Wang, Z.C., Zhang, B.C. and Qian, X.Z., ‘Oscillations of differential equations with deviating arguments’, Pan. Math. J. 2 (1992), 5978.
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Oscillation and nonoscillation of a delay differential equation

  • Chunhai Kou (a1) (a2), Weiping Yan (a2) and Jurang Yan (a2)

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