scholarly journals Global dynamics above the ground state energy for the combined power-type nonlinear Schrödinger equations with energy-critical growth at low frequencies

2021 ◽  
Vol 272 (1331) ◽  
Author(s):  
Takafumi Akahori ◽  
Slim Ibrahim ◽  
Hiroaki Kikuchi ◽  
Hayato Nawa
Keyword(s):  
Ground State ◽  
Critical Growth ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Global Dynamics ◽  
Schrödinger Equations ◽  
Power Type ◽  
Low Frequencies ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

We consider the combined power-type nonlinear Schrödinger equations with energy-critical growth, and study the solutions slightly above the ground state threshold at low frequencies, so that we obtain a so-called nine-set theory developed by Nakanishi and Schlag.

On a system of nonlinear Schrödinger equations with quadratic interaction and L2-critical growth

2021 ◽  
Author(s):  
Amin Esfahani
Keyword(s):  
Blow Up ◽  
Dynamical Behavior ◽  
Critical Growth ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Quadratic Interaction ◽  
Nonlinear Schrodinger Equations ◽  
Normalized Solutions

In this paper, we study the dynamical behavior of solutions of nonlinear Schrödinger equations with quadratic interaction and [Formula: see text]-critical growth. We give sharp conditions under which the existence of global and blow-up solutions are deduced. We also show the existence, stability, and blow-up behavior of normalized solutions of this system.

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