Non-degeneracy of the ground state solution on nonlinear Schrödinger equation

2021 ◽  
Vol 111 ◽  
pp. 106634
Author(s):  
Shuying Tian
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground State Solution ◽  
Nonlinear Schrodinger Equation ◽  
State Solution ◽  
Nonlinear Schrödinger

Solutions on a torus for a semilinear equation

2011 ◽  
Vol 141 (2) ◽  
pp. 371-382
Author(s):  
Geneviéve Allain ◽  
Anne Beaulieu
Keyword(s):  
Schrödinger Equation ◽  
Small Parameter ◽  
Periodic Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground State Solution ◽  
Nonlinear Schrodinger Equation ◽  
State Solution ◽  
Semilinear Equation

We are interested in the positive doubly periodic solutions, which are even in each variable, of a stationary nonlinear Schrödinger equation in ℝ2, with a small parameter. For any pair of periods (2a, 2b), we construct a branch of solutions that concentrate uniformly to the ground-state solution of the equation.

ON ONE BLOW UP POINT SOLUTIONS TO THE CRITICAL NONLINEAR SCHRÖDINGER EQUATION

2005 ◽  
Vol 02 (04) ◽  
pp. 919-962 ◽  
Author(s):  
FRANK MERLE ◽  
PIERRE RAPHAEL
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Ground State ◽  
Finite Time ◽  
Schrodinger Equation ◽  
Blow Up ◽  
Nonlinear Schrodinger Equation ◽  
Specific Class ◽  
Nonlinear Schrödinger ◽  
Existence And Stability

We consider the L2 critical nonlinear Schrödinger equation [Formula: see text] in the energy space H1. In the series of papers [11–15,18], we studied finite time blow up solutions for which lim t↑T < + ∞ |∇ u(t)|L2 = + ∞ and proved classification results of the blow up dynamics for the specific class of small super critical L2 mass initial data. We extend these results here to a wider class of finite time blow up solutions corresponding to the ones which accumulate at one point exactly the ground state mass. In particular, we prove the existence and stability of large L2 mass log-log type solutions which are believed to describe the generic blow up dynamics.

Sign in / Sign up

Export Citation Format

Share Document