The principal investigator will use a robust numerical technique based on the powerful mountain pass lemma to find multiple solutions of semilinear elliptic boundary value problems and in particular to find those solutions which are not local minima. A deeper theoretical understanding of the method and further expansion of the horizon of its applicability will be pursued. Solution structure is strongly dependent on the spatial dimension and the geometry of the domain. The existence and stability of steady state solutions in the case where multiple solutions exist is extremely delicate and important in most physical situations.
