scholarly journals Existence and stability of standing waves for coupled nonlinear Hartree type equations

2019 ◽  
Vol 60 (2) ◽  
pp. 021505 ◽  
Author(s):  
Santosh Bhattarai
Keyword(s):  
Standing Waves ◽  
Existence And Stability

scholarly journals Existence and Stability of Standing Waves For Schrödinger-Poisson-Slater Equation

2007 ◽  
Vol 7 (3) ◽  
Author(s):  
Hiroaki Kikuchi
Keyword(s):  
Variational Methods ◽  
Standing Wave ◽  
Nonlinear Term ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Standing Waves ◽  
Existence And Stability ◽  
Three Dimensional Space

AbstractWe study the existence and stability of standing wave for the Schrödinger-Poisson-Slater equation in three dimensional space. Let p be the exponent of the nonlinear term. Then we first show that standing wave exists for 1 < p < 5. Next, we show that when 1 < p < 7/3 and p ≠ 2, standing wave is stable for some ω > 0. We also show that when 7/3 < p < 5, standing wave is unstable for some ω > 0. Furthermore, we investigate the case of p = 2. We prove these results by using variational methods.

scholarly journals Existence and Stability of Standing Waves for Supercritical NLS with a Partial Confinement

2017 ◽  
Vol 353 (1) ◽  
pp. 229-251 ◽  
Author(s):  
Jacopo Bellazzini ◽  
Nabile Boussaïd ◽  
Louis Jeanjean ◽  
Nicola Visciglia
Keyword(s):  
Standing Waves ◽  
Existence And Stability ◽  
Partial Confinement
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