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: mud_abd@yahoo.com


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.

Abstract

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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