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

Department of Mathematics

African Institute for Mathematical Sciences of Senegal
NYU Shanghai
King Abdullah University of Science and Technology

Research output: Contribution to journal › Review article › peer-review

10 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.

Original language	English
Pages (from-to)	699-729
Number of pages	31
Journal	Analysis and Applications
Volume	15
Issue number	5
DOIs	https://doi.org/10.1142/S0219530516500056
State	Published - 2017.09.1

Keywords

fractional PDEs
Nonlinear Schrödinger equation
stability
standing waves
variational methods

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1142/S0219530516500056

Cite this

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title = "Orbital stability of standing waves of a class of fractional Schr{\"o}dinger equations with Hartree-type nonlinearity",

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.",

keywords = "fractional PDEs, Nonlinear Schr{\"o}dinger equation, stability, standing waves, variational methods",

author = "Yonggeun Cho and Fall, \{Mouhamed M.\} and Hichem Hajaiej and Markowich, \{Peter A.\} and Saber Trabelsi",

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AU - Cho, Yonggeun

AU - Fall, Mouhamed M.

AU - Hajaiej, Hichem

AU - Markowich, Peter A.

AU - Trabelsi, Saber

PY - 2017/9/1

Y1 - 2017/9/1

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.

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.

KW - fractional PDEs

KW - Nonlinear Schrödinger equation

KW - stability

KW - standing waves

KW - variational methods

UR - https://www.scopus.com/pages/publications/84976319628

U2 - 10.1142/S0219530516500056

DO - 10.1142/S0219530516500056

M3 - Review article

AN - SCOPUS:84976319628

SN - 0219-5305

VL - 15

SP - 699

EP - 729

JO - Analysis and Applications

JF - Analysis and Applications

IS - 5

ER -

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

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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