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Comparison theorems for higher-order neutral delay differential equations

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Abstract

In the paper, we combine new generalization of classical Philos and Staikos lemma together with suitable comparison technique to offer new oscillation criteria for \(n\)-th order neutral delay differential equation

$$\begin{aligned} \Big (r(t)\left[ z'(t)\right] ^{\gamma }\Big )^{(n-1)} +q(t)x^{\gamma }(\sigma (t))=0. \end{aligned}$$

The presented technique essentially simplifies the examination of the higher order differential equations.

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Acknowledgments

This work was supported by the Slovak Research and Development Agency under the contract No. APVV-0008-10 and No. APVV-0404-12.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00, Kosice, Slovakia

    B. Baculíková & J. Džurina

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  1. B. Baculíková
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  2. J. Džurina
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Correspondence to J. Džurina.

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Baculíková, B., Džurina, J. Comparison theorems for higher-order neutral delay differential equations. J. Appl. Math. Comput. 49, 107–118 (2015). https://doi.org/10.1007/s12190-014-0826-x

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  • DOI: https://doi.org/10.1007/s12190-014-0826-x

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