Abstract
We study the Cauchy problem for nonlinear Schrödinger equations with attractive inverse-power potentials. By using variational arguments, we first determine a sharp threshold of global well-posedness and blow-up for the equation in the mass-supercritical case. We next study the existence and orbital stability of standing waves for the problem in the mass-subcritical and mass-critical cases. In the mass-critical case, we give a detailed description of the blow-up behavior of standing waves when the mass tends to a critical value.
Citation
Van Duong Dinh. "On nonlinear Schrödinger equations with attractive inverse-power potentials." Topol. Methods Nonlinear Anal. 57 (2) 489 - 523, 2021. https://doi.org/10.12775/TMNA.2020.046
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