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

doi:10.1142/S0219530516500056

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

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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 language	English (US)
Pages (from-to)	699-729
Number of pages	31
Journal	Analysis and Applications
Volume	15
Issue number	05
DOIs	https://doi.org/10.1142/S0219530516500056
State	Published - May 4 2016

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abstract = "This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schr{\"o}dinger 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. {\textcopyright} 2015 World Scientific Publishing Company",

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AU - Fall, Mouhamed M.

AU - Hajaiej, Hichem

AU - Markowich, Peter A.

AU - Trabelsi, Saber

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PY - 2016/5/4

Y1 - 2016/5/4

N2 - 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

AB - 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

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JO - Analysis and Applications

JF - Analysis and Applications

IS - 05

ER -

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

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