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Oscillation Criteria for Certain Even Order Neutral Delay Differential Equations with Mixed Nonlinearities

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Listed:
  • Zhen-Lai Han
  • Yi-Bing Sun
  • Yan Zhao
  • Dian-Wu Yang

Abstract

We establish some oscillation criteria for the following certain even order neutral delay differential equations with mixed nonlinearities: rtzn-1tα-1zn-1t′+q0(t)(xτ0tα-1x(τ0(t))+q1t(x(τ1(t))β-1x(τ1(t))+q2t(x(τ2(t))γ-1x(τ2(t))=0, t≥t0, where z(t) = x(t) + p(t)x(σ(t)), n is even integer, and γ > α > β > 0. Our results generalize and improve some known results for oscillation of certain even order neutral delay differential equations with mixed nonlinearities.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:629074
    DOI: 10.1155/2014/629074
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    References listed on IDEAS

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    1. Shurong Sun & Tongxing Li & Zhenlai Han & Yibing Sun, 2011. "Oscillation of Second-Order Neutral Functional Differential Equations with Mixed Nonlinearities," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-15, January.
    2. Zhenlai Han & Tongxing Li & Chenghui Zhang & Ying Sun, 2011. "Oscillation Criteria for Certain Second‐Order Nonlinear Neutral Differential Equations of Mixed Type," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    3. Tongxing Li & Zhenlai Han & Chenghui Zhang & Hua Li, 2011. "Oscillation Criteria for Second‐Order Superlinear Neutral Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    4. 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.
    5. Ravi P. Agarwal & Said R. Grace & Donal O’Regan, 2000. "Oscillation Theory for Difference and Functional Differential Equations," Springer Books, Springer, number 978-94-015-9401-1, October.
    6. Shurong Sun & Tongxing Li & Zhenlai Han & Yibing Sun, 2011. "Oscillation of Second‐Order Neutral Functional Differential Equations with Mixed Nonlinearities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    7. Zhenlai Han & Tongxing Li & Chenghui Zhang & Ying Sun, 2011. "Oscillation Criteria for Certain Second-Order Nonlinear Neutral Differential Equations of Mixed Type," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-9, March.
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