Logarithmic Bose-Einstein condensates with harmonic potential

摘要

In this paper, by using a compactness method, we study the Cauchy problem of the logarithmic Schrodinger equation with harmonic potential. We then address the existence of ground states solutions as minimizers of the action on the Nehari manifold. Finally, we explicitly compute ground states (Gausson-type solution) and we show their orbital stability.