Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential

Abstract

This paper studies the mass-critical variable coefficient nonlinear Schrödinger equation. We first get the existence of the ground state by solving a minimization problem. Then we prove a compactness result by the variational characterization of the ground state solutions. In addition, we construct the blow-up solutions at the minimal mass threshold and further prove the uniqueness result on the minimal mass blow-up solutions which are pseudo-conformal transformation of the ground states.

Keywords

• variable coefficient nonlinear schrödinger equation
• minimal mass blow-up solutions
• variational characterization
• ground state
• compactness
• 35q55
• 35b44