ON BIFURCATION SOLUTIONS OF NONLINEAR FOURTH ORDER DIFFERENTIAL EQUATION
ALI H. ROSEN
Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq.
MUDHIR A. ABDUL HUSSAIN *
Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq.
*Author to whom correspondence should be addressed.
Abstract
In this article the bifurcation solutions of nonlinear fourth order differential equation has been investigated by using local method of Lyapunov -Schmidt. The reduced equation corresponding to the nonlinear fourth order differential equation has been found in the form of a nonlinear system of two algebraic equations. The classification of the solutions (equilibrium points) of this system has been discussed.
Keywords: Bifurcation theory, nonlinear systems, Local Lyapunov-Schmidt method