In the framework of the nonsmooth critical point theory for lower semi-continuous functionals, we propose a direct variational approach to investigate the existence of infinitely many weak solutions for a class of semi-linear elliptic equations with
logarithmic nonlinearity arising in physically relevant situations. Furthermore, we prove that there exists a unique positive solution which is radially symmetric and nondegenerate.
The soliton dynamics in the semiclassical limit for a weakly coupled nonlinear focusing Schrodinger systems in presence of a nonconstant potential is studied by taking as initial data some rescaled ground state solutions of an associate elliptic system.
We consider systems of weakly coupled Schrodinger equations with nonconstant potentials and we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary c
onditions for a sequence of least energy solutions to concentrate.
