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Esteban, M.J. and Lions, P. (1989) Stationary Solutions of Nonlinear Schrödinger Equations with an External Magnetic Field. In: Partial Differential Equations and the Calculus of Variations, Birkhäuser Boston, 401-449.
https://doi.org/10.1007/978-1-4684-9196-8_18

has been cited by the following article:

• TITLE: On Instability of Standing Waves for the Hartree Equation with a Magnetic Field

  AUTHORS: Rong Pang

  KEYWORDS: Hartree Equation, Magnetic Schr?dinger Equation, Standing Waves, Strong Instability, Blow-Up

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.6, June 24, 2026

  ABSTRACT: In this paper, we consider the strong instability of standing waves for the Hartree equation with a constant magnetic field. This equation arises as a mean-field model describing the evolution of many-body Bosonic systems. We first establish the variational characterization of ground states. Then, we prove that if ? 2 ? λ 2 S ω ( ? λ )| λ=1 ≤0 , the ground state standing wave e iωt ?( x ) is strongly unstable by blow-up, where S ω is the action functional, and ? λ ( x )= λ 3/2 ?( λx ) is the L 2 -invariant scaling.