Ground state for nonlinear Schrodinger equation with sign-changing and vanishing potential.

PDE Seminar
Tuesday, October 4, 2011 - 15:05
1 hour (actually 50 minutes)
Skiles 005
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, and Georgia Tech
We consider the stationary nonlinear Schrodinger equation when the potential changes sign and may vanish at infinity. We prove that there exists a sign-changing ground state and the so called energy doubling property for sign-changing solutions does not hold. Furthermore, we find that the ground state energy is not equal to the infimum of energy functional over the Nehari manifold. These phenomena are quite different from the case of positive potential.