Existence and stability of standing waves for the Choquard equation with partial confinement

2020 ◽  
pp. 1
Author(s):  
Lu Xiao ◽  
Qiuping Geng ◽  
Jun Wang ◽  
Maochun Zhu
Keyword(s):  
Standing Waves ◽  
Choquard Equation ◽  
Existence And Stability ◽  
Partial Confinement

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

scholarly journals Blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation

2020 ◽  
Vol 10 (1) ◽  
pp. 311-330 ◽  
Author(s):  
Feng Binhua ◽  
Ruipeng Chen ◽  
Jiayin Liu
Keyword(s):  
Blow Up ◽  
Standing Waves ◽  
Radial Solutions ◽  
Choquard Equation ◽  
Decomposition Theory ◽  
Profile Decomposition ◽  
Strong Instability

Abstract In this paper, we study blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation $$\begin{array}{} \displaystyle i\partial_t\psi- (-{\it\Delta})^s \psi+(I_\alpha \ast |\psi|^{p})|\psi|^{p-2}\psi=0. \end{array}$$ By using localized virial estimates, we firstly establish general blow-up criteria for non-radial solutions in both L2-critical and L2-supercritical cases. Then, we show existence of normalized standing waves by using the profile decomposition theory in Hs. Combining these results, we study the strong instability of normalized standing waves. Our obtained results greatly improve earlier results.

scholarly journals Instability of standing waves for a generalized Choquard equation with potential

2017 ◽  
Vol 58 (1) ◽  
pp. 011504 ◽  
Author(s):  
Zhipeng Cheng ◽  
Zifei Shen ◽  
Minbo Yang
Keyword(s):  
Standing Waves ◽  
Choquard Equation
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