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Asymptotic Dichotomy in a Class of Fourth‐Order Nonlinear Delay Differential Equations with Damping

Author

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  • Chengmin Hou
  • Sui Sun Cheng

Abstract

All solutions of a fourth‐order nonlinear delay differential equation are shown to converge to zero or to oscillate. Novel Riccati type techniques involving third‐order linear differential equations are employed. Implications in the deflection of elastic horizontal beams are also indicated.

Suggested Citation

  • Chengmin Hou & Sui Sun Cheng, 2009. "Asymptotic Dichotomy in a Class of Fourth‐Order Nonlinear Delay Differential Equations with Damping," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    • Handle: RePEc:wly:jnlaaa:v:2009:y:2009:i:1:n:484158
    DOI: 10.1155/2009/484158
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    Cited by:

    1. Mohamed Mazen & Mohamed M. A. El-Sheikh & Samah Euat Tallah & Gamal A. F. Ismail, 2025. "On the Oscillation of Fourth-Order Delay Differential Equations via Riccati Transformation," Mathematics, MDPI, vol. 13(3), pages 1-12, January.
    2. Jozef Dzurina & Blanka Baculikova & Irena Jadlovska, 2020. "Oscillatory solutions of fourth order advanced trinomial differential equations," Mathematische Nachrichten, Wiley Blackwell, vol. 293(6), pages 1110-1119, June.
    3. M. De la Sen, 2009. "On the Characterization of Hankel and Toeplitz Operators Describing Switched Linear Dynamic Systems with Point Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    4. Kun-Wen Wen & Gen-Qiang Wang & Sui Sun Cheng, 2010. "Asymptotic Dichotomyin a Class of Third‐Order Nonlinear Differential Equations with Impulses," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    5. Barakah Almarri & Ali Hasan Ali & António M. Lopes & Omar Bazighifan, 2022. "Nonlinear Differential Equations with Distributed Delay: Some New Oscillatory Solutions," Mathematics, MDPI, vol. 10(6), pages 1-10, March.

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