Stability, boundedness and periodic solutions to certain second order delay differential equations.

Authors

  • A. T. Ademola Obafemi Awolowo University.
  • Peter Olutola Arawomo University of Ibadan.
  • A. S. Idowu University of Ilorin.

DOI:

https://doi.org/10.4067/S0716-09172017000200257

Keywords:

Second order, Nonlinear differential equation, Uniform stability, Uniform ultimate boundedness, Existence of a unique periodic solutions

Abstract

Stability, boundedness and existence of a unique periodic solution to certain second order nonlinear delay differential equations is discussed. By employing Lyapunov's direct (or second) method, a complete Lyapunov functional is constructed and used to establish sufficient conditions, on the nonlinear terms, that guarantee uniform asymptotic stability, uniform ultimate boundedness and existence of a unique periodic solution. Obtained results complement many outstanding recent results in the literature. Finally, examples are given to show the effectiveness of our method and correctness of our results.

Author Biographies

A. T. Ademola, Obafemi Awolowo University.

Department of Mathematics.

Peter Olutola Arawomo, University of Ibadan.

Department of Mathematics.

A. S. Idowu, University of Ilorin.

Department of Mathematics.

 

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Published

2017-06-02

How to Cite

[1]
A. T. Ademola, P. O. Arawomo, and A. S. Idowu, “Stability, boundedness and periodic solutions to certain second order delay differential equations.”, Proyecciones (Antofagasta, On line), vol. 36, no. 2, pp. 257-282, Jun. 2017.

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Section

Artículos