Blow-up Solutions to Nonlinear Schrödinger Equation with a Potential

Abstract

This is a sequel to the paper “Characterization of the ground state to the intercritical NLS with a linear potential by the virial functional” by the same authors. We continue to study the Cauchy problem for a nonlinear Schrödinger equation with a potential. In the previous chapter, we investigated some minimization problems and showed global existence of solutions to the equation with initial data, whose action is less than the value of minimization problems and positive virial functional. In particular, we saw that such solutions are bounded. In this chapter, we deal with solutions to the equation with initial data, whose virial functional is negative contrary to the previous paper and show that such solutions are unbounded.