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**A. T. Ademola**

Department of Mathematics, Faculty of Science

Obafemi Awolowo University, Post Code 220005 Ile-Ife, Nigeria

**S. Moyo**

Institute for Systems Science & Research and Postgraduate Support Directorate

Durban University of Technology, Durban 4000, South Africa

**B. S. Ogundare**

Department of Mathematics, Faculty of Science

Obafemi Awolowo University, Post Code 220005 Ile-Ife, Nigeria

**M. O. Ogundiran**

Department of Mathematics, Faculty of Science

Obafemi Awolowo University, Post Code 220005 Ile-Ife, Nigeria

**O. A. Adesina**

Obafemi Awolowo University, Post Code 220005 Ile-Ife, Nigeria

In this work we consider a class of third order delay differential equations, where the nonlinear functions, especially the first two restoring terms, are sum of n multiple deviating arguments, the forcing term depends explicitly on the independent variable t for all i in [1..n], the last restoring term has variable coefficient, and deviating arguments vary for all i. By employing the direct technique of Lyapunov, where a complete Lyapunov functional is constructed and used, we obtain sufficient conditions that guarantee the existence of solutions which are periodic, uniformly asymptotically stable, uniformly ultimately bounded. The behaviour of solutions as t tends to infinity is studied. The obtained results are new and include many recent results in the literature. Finally, two examples are given to show the feasibility of our results.

- periodic solutions
- Third order nonlinear differential equation
- uniform stability
- uniform ultimate boundedness

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