International Journal of Differential Equations

Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations

A. T. Ademola, B. S. Ogundare, M. O. Ogundiran, and O. A. Adesina

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The behaviour of solutions to certain second order nonlinear delay differential equations with variable deviating arguments is discussed. The main procedure lies in the properties of a complete Lyapunov functional which is used to obtain suitable criteria to guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results are new and also complement related ones that have appeared in the literature. Moreover, examples are given to illustrate the feasibility and correctness of the main results.

Article information

Int. J. Differ. Equ., Volume 2016 (2016), Article ID 2843709, 10 pages.

Received: 29 April 2016
Accepted: 30 June 2016
First available in Project Euclid: 21 December 2016

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Ademola, A. T.; Ogundare, B. S.; Ogundiran, M. O.; Adesina, O. A. Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations. Int. J. Differ. Equ. 2016 (2016), Article ID 2843709, 10 pages. doi:10.1155/2016/2843709.

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