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Existence, non-existence and blow-up behaviour of minimizers for the mass-critical fractional non-linear Schrödinger equations with periodic potentials

  • Van Duong Dinh (a1) (a2)

Abstract

We consider the minimizing problem for the energy functional with prescribed mass constraint related to the fractional non-linear Schrödinger 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 behaviour of minimizers once the mass tends to a critical value.

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Existence, non-existence and blow-up behaviour of minimizers for the mass-critical fractional non-linear Schrödinger equations with periodic potentials

  • Van Duong Dinh (a1) (a2)

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