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Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments

  • Simona Fišnarová EMAIL logo and Robert Mařík
Published/Copyright: June 7, 2017
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Abstract

In this paper we derive oscillation criteria for the second order half-linear neutral differential equation

[r(t)Φ(z(t))]+c(t)Φ(x(σ(t)))=0,z(t)=x(t)+b(t)x(τ(t)),

where Φ(t) = |t|p−2t, p ≥ 2, is a power type nonlinearity. We improve recent results published in the literature by obtaining better oscillation constants and removing the usual condition σ(τ(t)) = τ(σ(t)). Two methods (comparison method and Riccati equation method) are used.


This research was supported by the Grant P201/10/1032 of the Czech Science Foundation.



(Communicated by Michal Fečkan)


Acknowledgement

We would like to thank the anonymous referees for valuable comments to the paper.

References

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Received: 2015-4-13
Accepted: 2016-1-19
Published Online: 2017-6-7
Published in Print: 2017-6-27

© 2017 Mathematical Institute Slovak Academy of Sciences

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