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

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