Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity

Yonggeun Cho, Mouhamed M. Fall, Hichem Hajaiej, Peter A. Markowich, Saber Trabelsi

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method. © 2015 World Scientific Publishing Company
Original languageEnglish (US)
Pages (from-to)699-729
Number of pages31
JournalAnalysis and Applications
Volume15
Issue number05
DOIs
StatePublished - May 4 2016

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