Skip to main content
SpringerLink
Log in

Pseudo Almost Periodic Solutions for a Class of Fourth-Order Nonlinear Differential Equations with a Deviating Argument

  • Original Research
  • Published:
Differential Equations and Dynamical Systems Aims and scope Submit manuscript

Abstract

This work is concerned with a class of fourth order semilinear ordinary differential equation with pseudo almost periodic environment and multiple delays. Specifically, we establish the existence and uniqueness of the pseudo almost periodic solutions. Furthermore, we discuss the global stability of the considered equation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Agarwal, R.P., Graceb, S.R., Manojlovicc, J.V.: Oscillation criteria for certain fourth order nonlinear functional differential equations. Math. Comput. Model. 44, 163–187 (2006)

    Article  MATH  Google Scholar 

  2. Amerio, L., Prouse, G.: Almost-Periodic Functions and Functional Analysis. Von Nostrand Reinhold Co., New York (1971)

    Book  Google Scholar 

  3. Ammar, B., Chérif, F., Alimi, A.M.: Existence and uniqueness of pseudo almost-periodic solutions of recurrent neural networks with time-varying coefficients and mixed delays. IEEE Transactions on neural networks and learning systems 23(1), 109–118 (2012)

    Article  Google Scholar 

  4. Amster, P., Mariani, M.C.: Oscillating solutions of a nonlinear fourth order ordinary differential equation. J. Math. Anal. Appl. 325, 1133–1141 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Carriao, P.C., Faria, L.F.O., Miyagaki, O.H.: Periodic solutions for extended Fisher–Kolmogorov and Swift–Hohenberg equations by truncature techniques. Non-linear Anal. 67, 3076–3083 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chérif, F.: A various types of almost periodic functions on Banach spaces. Int. Math. Forum 6(20), 953–985 (2011)

    MathSciNet  MATH  Google Scholar 

  7. Cronin, J.: Some mathematics of biological oscillations. SIAM Rev. 19, 100–137 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  8. Everitt, W.N., Markett, C., Littlejohn, L.L.: Properties of the solutions of the fourth-order Bessel-type differential equation. J. Math. Anal. Appl. 359, 252–264 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Fink, A.M.: Almost Periodic Differential Equations. Springer, Berlin (1974)

    MATH  Google Scholar 

  10. N’Guérékata, G.M.: Topics in Almost Automorphy. Springer, New York (2005)

    MATH  Google Scholar 

  11. Jin, S., Lu, S.: Periodic solutions for a fourth order p-Laplacian differential equation with a deviating argument. Nonlinear Anal. 69, 1710–1718 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Li, F., Li, Y.Z., Liang, Z.: Existence and multiplicity of solutions to 2mth-order ordinarydifferential equations. J. Math. Anal. Appl. 331, 958–977 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Li, B.: Uniqueness and stability of a limit cycle for a third-order dynamical system arising in neuron modeling. Nonlinear Anal. 5, 13–19 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  14. Mawhin, J., Zanolin, F.: A continuation approach to fourth order superlinear periodic boundary value problems. Topol. Methods Nonlinear Anal. 2, 55–74 (1993)

    MathSciNet  MATH  Google Scholar 

  15. Peletier, L.A., Troy, W.C.: Spatial patterns described by the Fisher-Kolmogorov equation: periodic solutions. SIAM J. Math. Anal. 28, 1317–1353 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  16. Xiong, W., Yueb, G.: Almost periodic solutions for a class of fourth-order nonlinear differential equations with a deviating argument. Comput. Math. Appl. 60, 1184–1190 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Yao, Q.: Existence, multiplicity and infinite solvability of positive solutions to a nonlinear fourth-order periodic boundary value problem. Nonlinear Anal. 63, 237–246 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang, C.: Pseudo almost periodic functions and their applications. Ph.D. thesis, University of Western Ontario (1992)

  19. Zhang, C.: Almost Periodic Type Functions and Ergodicity. Kluwer Academic Publishers and Science Press, Beijing (2003)

    Book  MATH  Google Scholar 

  20. Tomoshenko, S., Gere, S.: Theory of Elastic Stability, 2nd edn. McGraw Hill, New York (1961)

    Google Scholar 

Download references

Acknowledgments

I would like to thank the anonymous reviewer and the editor for their valuable suggestions and comments helping to ameliorate the quality and the presentation of the paper.

Author information

Authors and Affiliations

  1. ISSATs and Laboratory of Mathematical Physic, Specials Functions and Applications, LR11ES35, Ecole Supérieure des Sciences et de Technologie de Hammam-Sousse, Université de Sousse, Sousse, Tunisia

    Farouk Chérif

Authors
  1. Farouk Chérif
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Farouk Chérif.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chérif, F. Pseudo Almost Periodic Solutions for a Class of Fourth-Order Nonlinear Differential Equations with a Deviating Argument. Differ Equ Dyn Syst 24, 81–97 (2016). https://doi.org/10.1007/s12591-014-0216-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12591-014-0216-8

Keywords

Search

Navigation