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Oscillation of neutral delay differential equations

Published online by Cambridge University Press:  17 April 2009

Jianshe Yu ,
Zhicheng Wang  and
Chuanxi Qian
Jianshe Yu
Affiliation:
Department of Appllied MathematicsHunan UniversityChangsha Hunan 410082 PeoplesRepublic of China
Zhicheng Wang
Affiliation:
Department of MathematicsThe University of Rhode IslandKingston Rhode Island 02881United States of America
Chuanxi Qian
Affiliation:
Department of MathematicsThe University of Rhode IslandKingston Rhode Island 02881United States of America
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Abstract

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Consider the following neutral delay differential equation

where P ∈ ℝ, T ∈ (0, ∞), σ ∈ (0, ∞) and Q ∈ C[(t0, ∞), [0, ∞)]. We obtain a sufficient condition for the oscillation of all solutions of Equation (*) with P = −1, which does not require that

But, for the cases −1 < P < 0 and P < −1, we show that (**) is a necessary condition for the oscillation of all solutions of Equation (*). These new results solve some open problems in the literature.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 2 , April 1992 , pp. 195 - 200
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Chuanxi, Q. and Ladas, G., ‘Oscillations of neutral differential equations with variable coefficients’, Appl. Anal. 32 (1989), 215–228.CrossRefGoogle Scholar
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[3]Koplatadze, R.G. and Chanturia, T.A., ‘On oscillatory and monotonic solutions of first-order differential equations with retarded arguments’, Differentsial'nye Uravneniya 8 (1982), 1463–1465. (in Russian).Google Scholar