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

Yonggeun Cho, Mouhamed M. Fall, Hichem Hajaiej, Peter A. Markowich and Saber Trabelsi
Analysis and applications, Vol.15(5), pp.699-729
01/09/2017

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrodinger 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.

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