We investigate the following logarithmic Schrodinger equation -Delta u + V(x)u = u log u(2), x is an element of R-N. The classical variational methods cannot be applied directly, because the corresponding energy functional is not well defined in H-1 (R-N). By using direction derivative and constrained minimization method, we prove the existence of positive and sign-changing solutions in H-1 (R-N) under different types of potential. Moreover, if the potential is radially symmetric, we als...
