Sharp conditions for a class of nonlinear Schrödinger equations

Abstract

This paper studies a class of nonlinear Schrödinger equations in two space dimensions. By constructing a variational problem and the so-called invariant manifolds of the evolution flow, we get a sharp condition for global existence and blow-up of solutions.

Keywords

• nonlinear schrödinger equations
• global existence
• blow-up
• sharp conditions
• invariant manifolds