| Abstract: |
| The talk discusses general non-uniqueness results for normalized ground states of nonlinear Schr\odinger equations with power nonlinearity. Basically, we show that, when in the $L^2-$subcritical regime ground states exist at every mass, for nonlinearity powers close to the $L^2$--critical exponent there is at least one value of the mass for which ground states are non-unique. As a consequence, whenever such non--uniqueness occurs there exist action ground states that are not normalized ground states. These results have been obtained both when the problem is set on metric graphs (compact and non--compact) and when it is posed on polygons with homogeneous Neumann boundary conditions. |
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