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Advances in Pure and Applied Mathematics

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Stability and boundedness of solutions of a certain n-dimensional nonlinear delay differential system of third-order

Ayman M. Mahmoud
  • Department of Mathematics, Faculty of Science, New Valley Branch, Assiut University, New Valley, El-khargah 72111, Egypt
  • Email:
/ Cemil Tunç
  • Corresponding author
  • Department of Mathematics, Faculty of Science, Yuzuncu Yil University, 65080, Van, Turkey
  • Email:
Published Online: 2015-10-20 | DOI: https://doi.org/10.1515/apam-2014-0033


In this paper, by defining Lyapunov functionals, we investigate proper sufficient conditions for the uniform stability of the zero solution, and also for the uniform boundedness and uniform ultimate boundedness of all solutions of a certain third-order nonlinear vector delay differential equation of the type X˙˙˙ + AX˙˙ + G(X˙) + H(X(t - r)) = P(t).

Keywords: Uniform stability; ultimate boundedness; Lyapunov functionals; vector differential equations; delay differential equations

MSC: 34K20; 34D20

About the article

Received: 2014-07-02

Accepted: 2015-07-31

Published Online: 2015-10-20

Published in Print: 2016-01-01

Citation Information: Advances in Pure and Applied Mathematics, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam-2014-0033. Export Citation

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