Journal of Nonlinear Analysis and Application

Volume 2018, No. 1 (2018), Pages 48-56

Article ID jnaa-00395, 9 Pages

doi: 10.5899/2018/jnaa-00395

Research Article

On Bifurcation of Periodic Solutions of Nonlinear Fourth Order Ordinary Differential Equation

Mudhir A. Abdul Hussain1 *, Thaar H. Qaasim1

1Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, IRAQ.

* Corresponding author. Email address:

Received: 18 June 2017; Accepted: 14 September 2017

Copyright © 2018 Mudhir A. Abdul Hussain and Thaar H. Qaasim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this article we are interested in the study of bifurcation of periodic solutions of nonlinear fourth order differential equation by using local method of Lyapunov -Schmidt. We showed that the reduced equation corresponding to the nonlinear fourth order differential equation is given by a nonlinear system of four algebraic equations. The classification of the solutions (equilibrium points) of this system has been discussed.

Keywords: Bifurcation theory; Nonlinear systems; Local Lyapunov-Schmidt method.


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