Multiple solutions for logarithmic Schrödinger equations

Abstract

Abstract We investigate the following logarithmic Schrödinger equation The classical variational methods cannot be applied directly, because the corresponding energy functional is not well defined in . By using direction derivative and constrained minimization method, we prove the existence of positive and sign-changing solutions in under different types of potential. Moreover, if the potential is radially symmetric, we also construct infinitely many nodal solutions in .