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Oscillatory Behavior of Second‐Order Nonlinear Neutral Differential Equations

Author

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  • Tongxing Li
  • Yuriy V. Rogovchenko

Abstract

We study oscillatory behavior of solutions to a class of second‐order nonlinear neutral differential equations under the assumptions that allow applications to differential equations with delayed and advanced arguments. New theorems do not need several restrictive assumptions required in related results reported in the literature. Several examples are provided to show that the results obtained are sharp even for second‐order ordinary differential equations and improve related contributions to the subject.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:143614
    DOI: 10.1155/2014/143614
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    References listed on IDEAS

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    1. Ravi P. Agarwal & Said R. Grace & Donal O’Regan, 2002. "Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations," Springer Books, Springer, number 978-94-017-2515-6, March.
    2. 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.
    3. 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, March.
    4. 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).
    5. Shurong Sun & Tongxing Li & Zhenlai Han & Hua Li, 2012. "Oscillation Theorems for Second‐Order Quasilinear Neutral Functional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Shurong Sun & Tongxing Li & Zhenlai Han & Hua Li, 2012. "Oscillation Theorems for Second-Order Quasilinear Neutral Functional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, July.
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