Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations
The author studies the existence and symmetry property of multi-bump solutions of the equation \(-\Delta v+\lambda V(x)v=v^p\), \(v>0\), in \(\mathbb{R}^N\). Especially when the potential \(V\) is radially symmetric, i.e., \(V(x)=V(|x|)\), multi-bump solutions are constructed with bumps concentrated on a simply-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. Consequently, many non-radial solutions of the equation are constructed with prescribed exact symmetry.
scientific article; zbMATH DE number 1389119
scientific article