Bifurcation from double eigenvalue for nonlinear equation with third-order nondegenerate singularity

In this paper, the steady state bifurcation from a double eigenvalue for nonlinear equation with singularity being second-order fully degenerate and third-order nondegenerate is investigated. By the normalized Lyapunov-Schmidt reduction method, the precise criteria for the existence and nonexistence of bifurcation and the topological properties of regular bifurcated branches are obtained.