Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615940 | Journal of Mathematical Analysis and Applications | 2014 | 13 Pages |
Abstract
In this paper, we consider the nonlinear fractional Schrödinger equations with Hartree type nonlinearity. We obtain the existence of standing waves by studying the related constrained minimization problems via applying the concentration-compactness principle. By symmetric decreasing rearrangements, we also show that the standing waves, up to 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Dan Wu,