Existence and Symmetry of Multi-bump Solutions for Nonlinear Schrödinger Equations

We study the existence and symmetry property of multi-bump solutions of Especially when the potential V is radially symmetric, multi-bump solutions are constructed with bumps concentrating on a single connected component of the set of global minimum points of V. Furthermore, conditions are given to assure that the multi-bump solutions obtained have prescribed subgroups of O(N) as their exact symmetry.