Abstract
In this paper, the bifurcation solutions of the boundary condition problem has been studied by using the local method from Lyapunov-Schmidt. We reduce the bifurcation equation and make it in the form of Operator equation. In addition, the finite dimensional reduction theorem for the bifurcation equation is given by the nonlinear system of fourth order equations. We investigate the analysis system of the bifurcation equation, we also find the Discriminant set of corresponding to the nonlinear differential equation by using (Maple 2016) program. The classification of the equilibrium points of the Dynamical System are discussed. And the phase portrait of boundary condition problem is found in three dimensional.
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