Blow-up Behavior For The Solutions Of Nonlinear Schr(?)dinger Equations With Potential

In present paper, we study the existence and dynamical properties of the blow-upsolutions for the nonlinear Schrodinger equation with potential in energy space.In introduction, first of all, we present the physical background and someknown results on the nonlinear Schrodinger equation with potential. Secondly,we recall some results on the classical nonlinear Schrodinger equation. Finally,we introduce some conclusions on the ground of nonlinear Schrodinger equation.In chapter 2, the existence of blow-up solutions of nonlinear Schrodingerequation with potential is established, which is based on the conservation of massand energy. In chapter 3, We studied the the qualitative properties of blow-up solutions ofcritical nonlinear Schrodinger equation with potential. For the radially symmetriccase, we prove that the original point 0 is a blow-up point and that the existenceof concentration at the blow-up point. For the general case, the existence ofblow-up point and concentration is also obtained.