Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-23T21:19:18.562Z Has data issue: false hasContentIssue false

Some further results on oscillation of neutral differential equations

Published online by Cambridge University Press:  17 April 2009

Jianshe Yu
Affiliation:
Department of Applied Mathematics Hunan, University Changsha Hunan, 410082, People's Republic of China
Zhicheng Wang
Affiliation:
Department of Applied Mathematics Hunan, University Changsha Hunan, 410082, People's Republic of China
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We obtain new sufficient conditions for the oscillation of all solutions of the neutral differential equation with variable coefficients

where P, Q, RC([t0, ∞), R+), r ∈ (0, ∞) and τ, σ ∈ [0, ∞). Our results improve several known results in papers by: Chuanxi and Ladas; Lalli and Zhang; Wei; Ruan.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Chuanxi, Q. and Ladas, G., ‘Oscillation in differential equations with positive and negative coefficients’, Canad. Math. Bull 33 (1990), 442450.Google Scholar
[2]Erbe, L.H. and Zhang, B.G., ‘Oscillation for first order linear differential equations with deviating arguments’, Differential Integral Equations 1 (1988), 305314.CrossRefGoogle Scholar
[3]Farrell, K., Grove, E.A. and Ladas, G., ‘Neutral delay differential equations with positive and negative coefficients’, Appl. Anal. 27 (1988), 181197.CrossRefGoogle Scholar
[4]Györi, I. and Ladas, G., Oscillation theory of delay differential equations with applications (Clarendon Press, Oxford, 1991).CrossRefGoogle Scholar
[5]Chao, J., ‘Oscillation of linear differential equations with deviating arguments’, Theory Practice Math. 1 (1991), 3241.Google Scholar
[6]Lalli, B.S. and Zhang, B.G., ‘Oscillation of first order neutral differential equations’, Appl. Anal. 39 (1990), 265274.CrossRefGoogle Scholar
[7]Ruan, S.G., ‘Oscillations for first order neutral differential equations with variable coefficients’, Bull. Austral. Math. Soc. 43 (1991), 147152.CrossRefGoogle Scholar
[8]Wei, J.J., ‘Sufficient and necessary conditions for the oscillation of first order differential equations with deviating arguments and applications’, Acta. Math. Sinica 32 (1989), 632638.Google Scholar
[9]Yu, J.S., ‘Neutral differential equations with positive and negative coefficients’, Acta. Math. Sinica 34 (1991), 517523.Google Scholar