Steady state bifurcations for phase field crystal equations with underlying two dimensional kernel

This paper is concerned with the study of some properties of stationary solutions to Phase Field Crystal Equations bifurcating from a trivial solution. It is assumed that at this trivial solution, the kernel of the underlying linearized operator has dimension two. By means of the multiparameter method, we give a second order approximation of these bifurcating solutions and analyse their stability properties. The main result states that the stability of these solutions can be described by the variation of a certain angle in a two dimensional parameter space. The behaviour of the parameter curve is also investigated.