Stability of standing waves for logarithmic Schr\"odinger equation with   attractive delta potential
  We consider the one-dimensional logarithmic Schr\"odinger equation with a delta potential. Global well-posedness is verified for the Cauchy problem in H1(R) and in an appropriate Orlicz space. In the attractive case, we prove orbital stability of the ground states via variational approach. 
Jaime Angulo Pava and Alex Hernandez Ardila
math.AP