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Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations

Author

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  • Tongxing Li
  • Zhenlai Han
  • Chenghui Zhang
  • Hua Li

Abstract

Some oscillation criteria are established for the second-order superlinear neutral differential equations ( ð ‘Ÿ ( ð ‘¡ ) | 𠑧 ′ ( ð ‘¡ ) | ð ›¼ − 1 𠑧 ′ ( ð ‘¡ ) ) ′ + ð ‘“ ( ð ‘¡ , ð ‘¥ ( 𠜎 ( ð ‘¡ ) ) ) = 0 , ð ‘¡ ≥ ð ‘¡ 0 , where 𠑧 ( ð ‘¡ ) = ð ‘¥ ( ð ‘¡ ) + ð ‘ ( ð ‘¡ ) ð ‘¥ ( ð œ ( ð ‘¡ ) ) , ð œ ( ð ‘¡ ) ≥ ð ‘¡ , 𠜎 ( ð ‘¡ ) ≥ ð ‘¡ , ð ‘ âˆˆ ð ¶ ( [ ð ‘¡ 0 , ∞ ) , [ 0 , ð ‘ 0 ] ) , and ð ›¼ ≥ 1 . Our results are based on the cases ∫ ∞ ð ‘¡ 0 1 / ð ‘Ÿ 1 / ð ›¼ ( ð ‘¡ ) d ð ‘¡ = ∞ or ∫ ∞ ð ‘¡ 0 1 / ð ‘Ÿ 1 / ð ›¼ ( ð ‘¡ ) d ð ‘¡ < ∞ . Two examples are also provided to illustrate these results.

Suggested Citation

  • Tongxing Li & Zhenlai Han & Chenghui Zhang & Hua Li, 2011. "Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-17, March.
    • Handle: RePEc:hin:jnlaaa:367541
    DOI: 10.1155/2011/367541
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    Cited by:

    1. Zhen-Lai Han & Yi-Bing Sun & Yan Zhao & Dian-Wu Yang, 2014. "Oscillation Criteria for Certain Even Order Neutral Delay Differential Equations with Mixed Nonlinearities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Asylzat Kopzhassarova & Abdizhakhan Sarsenbi, 2012. "Basis Properties of Eigenfunctions of Second‐Order Differential Operators with Involution," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Tongxing Li & Yuriy V. Rogovchenko, 2014. "Oscillatory Behavior of Second‐Order Nonlinear Neutral Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Simona Fišnarová & Robert Mařík, 2014. "On Eventually Positive Solutions of Quasilinear Second‐Order Neutral Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. I. Orazov & A. Shaldanbayev & M. Shomanbayeva, 2013. "About the Nature of the Spectrum of the Periodic Problem for the Heat Equation with a Deviating Argument," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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