Stability of standing waves for nonlinear Schrödinger equations with unbounded potentials

2000 ◽  
Vol 51 (3) ◽  
pp. 498-503 ◽  
Author(s):  
J. Zhang
Keyword(s):  
Standing Waves ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

scholarly journals Nonlinear Schrödinger equations with strongly singular potentials

2010 ◽  
Vol 140 (4) ◽  
pp. 707-721 ◽  
Author(s):  
Jacopo Bellazzini ◽  
Claudio Bonanno
Keyword(s):  
Angular Momentum ◽  
Standing Waves ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Cylindrically Symmetric ◽  
Nonlinear Schrodinger Equations ◽  
Image Position ◽  
Strongly Singular Potentials

We look for standing waves for nonlinear Schrödinger equationswith cylindrically symmetric potentials g vanishing at infinity and non-increasing, and a C1 nonlinear term satisfying weak assumptions. In particular, we show the existence of standing waves with non-vanishing angular momentum with prescribed L2 norm. The solutions are obtained via a minimization argument, and the proof is given for an abstract functional which presents a lack of compactness. As a specific case, we prove the existence of standing waves with non-vanishing angular momentum for the nonlinear hydrogen atom equation.

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