期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 411, 期 2, 页码 530-542出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2013.09.054
关键词
Fractional nonlinear Schrodinger equation; Hartree; Standing wave; Stability; Concentration-compactness
资金
- National Center of Mathematics and Interdisciplinary Sciences
- CAS
In this paper, we consider the nonlinear fractional Schrodinger 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. (C) 2013 Elsevier Inc. All rights reserved.
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