On the blow‐up for nonlinear Schrödinger equation with inhomogeneous perturbation

Abstract

We devote to the analysis of blow‐up solutions for the nonlinear Schrödinger equation with inhomogeneous perturbation. Firstly, we get the sharp threshold of global existence and blow‐up for the Cauchy problem. Then, we show the mass concentration properties and the limiting behavior of blow‐up solutions. At last, we prove the nonexistence of the minimal mass blow‐up solution by using the limiting behavior of blow‐up solutions.