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https://doi.org/10.1016/s0294-1449(16)30422-x

has been cited by the following article:

• TITLE: Stability of Standing Waves for the Nonlinear Schrödinger Equation with Mixed Power-Type and Hartree-Type Nonlinearities

  AUTHORS: Chunyang Yan

  KEYWORDS: Nonlinear Schrödinger Equation, Concentration Compactness Principle, Orbital Stability

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.10, October 22, 2024

  ABSTRACT: This paper studies the existence of stable standing waves for the nonlinear Schrödinger equation with Hartree-type nonlinearity i ∂ t ψ+Δψ+ | ψ | p ψ+( | x | −γ ∗ | ψ | 2 )ψ=0,   ( t,x )∈[ 0,T )× ℝ N . Where ψ=ψ( t,x ) is a complex valued function of ( t,x )∈ ℝ + × ℝ N . The parameters N≥3 , 0<p< 4 N and 0<γ<min{ 4,N } . By using the variational methods and concentration compactness principle, we prove the orbital stability of standing waves.