Existence and stability of standing waves for nonlinear fractional Schr\"odinger equations with Hartree type nonlinearity

By Dan Wu. 2012

52 citations recorded by the source corpus.

In this paper, we consider the nonlinear fractional Schr\"odinger equations with Hartree type nonlinearity. We obtain the existence of standing waves by studying the related constrained minimization problems by applying the concentration-compactness principle. Via symmetric decreasing rearrangements, we also show that the standing waves, up to a translations and phases, are positive symmetric nonincreasing functions. Moreover, we prove that the set of minimizers is a stable set for the initial value problem of the equations, that is, a solution whose initial data is near the set will remain near it for all time.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0bf263e4a6f1dda4baa9645472e516ec9e8bf15d

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In Applied Mathematics

1. Pietro d'Avenia
2. Marco Squassina
3. Gaetano Siciliano
4. Patrick Winkert
5. Hongyu Ye
6. Tingjian Luo

In Mathematical Physics

1. Gaetano Siciliano
2. Pietro d'Avenia
3. Marco Squassina
4. Hongyu Ye
5. Claudianor Oliveira Alves
6. Tingjian Luo

Citations in the corpus

• On fractional Choquard equations (2014, background): “This topic was recently investigated in [28] in the case p = 2 and with α ∈ (N−2s,N), see the introduction therein for the physical motivations.”