Prof. Zhi-Qiang Wang，Utah State University, USA

We discuss the existence of localized nodal solutions for the semiclassical nonlinear Schr?dinger equation with the potential V assumed to have a local minimum point P. As $\epsilon \to 0$, we construct an infinite sequence of localized nodal solutions clustered at P and these solutions are of higher topological type in the sense that they are obtained from a minimax characterization of higher dimensional symmetric linking structure. Our method is rather robust without using any non-degeneracy condition.