Abstract and Applied Analysis

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

Chengmin Hou and Sui Sun Cheng

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 484158, 7 pages.

Dates
First available in Project Euclid: 16 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1268745563

Digital Object Identifier
doi:10.1155/2009/484158

Mathematical Reviews number (MathSciNet)
MR2516005

Zentralblatt MATH identifier
1173.34350

Citation

Hou, Chengmin; Cheng, Sui Sun. Asymptotic Dichotomy in a Class of Fourth-Order Nonlinear Delay Differential Equations with Damping. Abstr. Appl. Anal. 2009 (2009), Article ID 484158, 7 pages. doi:10.1155/2009/484158. https://projecteuclid.org/euclid.aaa/1268745563


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References

  • A. Tiryaki and M. F. Aktaş, ``Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping,'' Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 54--68, 2007.
  • G. S. Ladde, V. Lakshmikantham, and B. G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, vol. 110 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1987.
  • Z. G. Ouyang and Y. K. Li, ``Monotone solutions of even-order delay differential equations,'' Journal of Mathematical Research and Exposition, vol. 24, no. 2, pp. 321--327, 2004.