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Oscillation of Second-Order Nonlinear Neutral Dynamic Equations with Noncanonical Operators

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Abstract

The study of half-linear differential equations has become an important area of research due to the fact that such equations occur in a variety of real-world problems such as in the study of \(p\)-Laplace equations, non-Newtonian fluid theory, and the turbulent flow of a polytrophic gas in a porous medium. On the basis of these background details, we study oscillatory behavior of a class of second-order neutral functional dynamic equations on a time scale. New criteria improve and complement related results reported in the literature. Some examples are included to illustrate the results obtained. In particular, an example regarding the second-order neutral differential equation is also provided to show that these theorems improve those in the continuous case.

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Acknowledgments

This research is supported by NNSF of P. R. China (Grant Nos. 61034007, 51277116, 50977054). The authors express their sincere gratitude to the Editors for useful comments that helped to accentuate important details.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, Shandong, People’s Republic of China

    Chenghui Zhang & Tongxing Li

  2. Department of Mathematics, Texas A&M University–Kingsville, 700 University Blvd., Kingsville, TX, 78363-8202, USA

    Ravi P. Agarwal

  3. Department of Mathematics and Statistics, Missouri S&T, Rolla, MO, 65409-0020, USA

    Martin Bohner

Authors
  1. Chenghui Zhang
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  2. Ravi P. Agarwal
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  3. Martin Bohner
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  4. Tongxing Li
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Correspondence to Tongxing Li.

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Communicated by Shangjiang Guo.

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Zhang, C., Agarwal, R.P., Bohner, M. et al. Oscillation of Second-Order Nonlinear Neutral Dynamic Equations with Noncanonical Operators. Bull. Malays. Math. Sci. Soc. 38, 761–778 (2015). https://doi.org/10.1007/s40840-014-0048-2

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  • DOI: https://doi.org/10.1007/s40840-014-0048-2

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