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arXiv · 1903.04636

On nonlinear Schr\"odinger equations with attractive inverse-power potentials

Van Duong Dinh
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Abstract

We study the Cauchy problem for nonlinear Schr\"odinger 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 non-existence of minimizers for the energy functional with prescribed mass constraint. In the mass-critical case, we also study the blow-up behavior of minimizers when the mass tends to a critical value.

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Van Duong Dinh. 2019-03-11. On nonlinear Schr\"odinger equations with attractive inverse-power potentials. https://arxiv.org/abs/1903.04636

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