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arXiv · 1912.08750

Existence, non-existence and blow-up behavior of minimizers for the mass-critical fractional nonlinear Schr\"odinger equations with periodic potentials

Van Duong Dinh
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Abstract

We consider the minimizing problem for the energy functional with prescribed mass constraint related to the fractional nonlinear Schr\"odinger equation with periodic potentials. Using the concentration-compactness principle, we show a complete classification for the existence and non-existence of minimizers for the problem. In the mass-critical case, under a suitable assumption of the potential, we give a detailed description of blow-up behavior of minimizers once the mass tends to a critical value.

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Van Duong Dinh. 2019-12-18. Existence, non-existence and blow-up behavior of minimizers for the mass-critical fractional nonlinear Schr\"odinger equations with periodic potentials. https://arxiv.org/abs/1912.08750

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