## Differential and Integral Equations

### Nonexistence of scattering and modified scattering states for some nonlinear Schrödinger equation with critical homogeneous nonlinearity

#### Abstract

We consider large time behavior of solutions to the nonlinear Schrödinger equation with a homogeneous nonlinearity of the critical order which is not necessarily a polynomial. We treat the case in which the nonlinearity contains non-oscillating factor $|u|^{1+2/d}$. The case is excluded in our previous studies. It turns out that there are no solutions that behave like a free solution with or without logarithmic phase corrections. We also prove nonexistence of an asymptotic free solution in the case that the gauge invariant nonlinearity is dominant, and give a finite time blow-up result.

#### Article information

Source
Differential Integral Equations, Volume 32, Number 3/4 (2019), 121-138.

Dates
First available in Project Euclid: 23 January 2019