Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 411, Issue 2, Pages 530-542Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2013.09.054
Keywords
Fractional nonlinear Schrodinger equation; Hartree; Standing wave; Stability; Concentration-compactness
Categories
Funding
- National Center of Mathematics and Interdisciplinary Sciences
- CAS
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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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