We present a stability result for ground states of a Schrodinger-Poisson system in $(2+1)$ dimension, modelling the propagation of a light beam through a liquid crystal with nonlocal nonlinear response. A new estimate for perturbations of the medium configuration allows to explicitly prove strict positivity of the second derivative of the action on a ground state. In addition we prove existence of a ground state with frequency σ for any σ ∈ (0,1) by a continuity method.
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Sergio Moroni (2024) studied this question.
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